Artykuły w czasopismach: „Resolving dominating set”

1

Mohamad, Jerson, and Helen Rara. "1-Movable Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 418–29. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4671.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. A set W ⊆ V (G) is a resolving hop dominating set of G if W is a resolving set in G and for every vertex v ∈ V (G) \ W there exists u ∈ W such that dG(u, v) = 2. A set S ⊆ V (G) is a 1-movable resolving hop dominating set of G if S is a resolving hop dominating set of G and for every v ∈ S, either S \ {v} is a resolving hop dominating set of G or there exists a vertex u ∈ ((V (G) \ S) ∩ NG(v)) such that (S \ {v}) ∪ {u} is a resolving hop dominating set of G. The 1-movable resolving hop domination number of G, denoted by γ 1 mRh(G) is the smallest cardinality of a 1-movable resolving hop dominating set of G. This paper presents the characterization of the 1-movable resolving hop dominating sets in the join, corona and lexicographic product of graphs. Furthermore, this paper determines the exact value or bounds of their corresponding 1-movable resolving hop domination number.

Style APA, Harvard, Vancouver, ISO itp.

2

Sumaoy, Helyn Cosinas, and Helen Rara. "On Movable Strong Resolving Domination in Graphs." European Journal of Pure and Applied Mathematics 15, no. 3 (2022): 1201–10. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4440.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. A strong resolving dominating set S is a 1-movable strong resolving dominating set of G if for every v ∈ S, either S \ {v} is a strong resolving dominating set or there exists a vertex u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a strong resolving dominating set of G. The minimum cardinality of a 1-movable strong resolving dominating set of G,denoted by γ1 msR(G) is the 1-movable strong resolving domination number of G. A 1-movable strong resolving dominating set with cardinality γ1msR(G) is called a γ1msR-set of G. In this paper, we study this concept and the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the 1-movable strong resolvingdominating sets in these types of graphs and determine the exact values of their 1-movable strong resolving domination numbers.

Style APA, Harvard, Vancouver, ISO itp.

3

Humaizah, R., Dafik, A. I. Kristiana, I. H. Agustin, and E. Y. Kurniawati. "On the resolving strong domination number of some wheel related graphs." Journal of Physics: Conference Series 2157, no. 1 (2022): 012015. http://dx.doi.org/10.1088/1742-6596/2157/1/012015.

Pełny tekst źródła

Streszczenie:

Abstract This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V(G) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of graph G, denoted by γrst (G), is the minimum cardinality of resolving strong dominating set of G. In this paper, we determine the resolving strong domination number of some wheel related graphs, namely helm graph Hn , gear graph Gn , and flower graph Fln . Through this paper, we will use the notations γst (G) and dim(G) which show the strong domination and dimension numbers.

Style APA, Harvard, Vancouver, ISO itp.

4

Cabaro, Jean Mansanadez, and Helen Rara. "Restrained 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs." European Journal of Pure and Applied Mathematics 15, no. 3 (2022): 1047–53. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4451.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A set S ⊆ V (G) is a restrained 2-resolving dominating set in G if S is a 2-resolving dominating set in G and S = V (G) or ⟨V (G)\S⟩ has no isolated vertex. The restrained 2R-domination number of G, denoted by γr2R(G), is the smallest cardinality of a restrained 2-resolving dominating set in G. Any restrained 2-resolving dominating set of cardinality γr2R(G) is referred to as a γr2R-set in G. This study deals with the concept of restrained 2-resolving dominating set of a graph. It characterizes the restrained 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the restrained 2-resolving domination number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

5

Monsanto, Gerald Bacon, and Helen M. Rara. "Resolving Restrained Domination in Graphs." European Journal of Pure and Applied Mathematics 14, no. 3 (2021): 829–41. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3985.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. Brigham et al. [3] defined a resolving dominating setas a set S of vertices of a connected graph G that is both resolving and dominating. A set S âŠ† V (G) is a resolving restrained dominating set of G if S is a resolving dominating set of G and S = V (G) or hV (G) \ Si has no isolated vertex. In this paper, we characterize the resolving restrained dominating sets in the join, corona and lexicographic product of graphs and determine the resolving restrained domination number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

6

Monsanto, Gerald Bacon, Penelyn L. Acal, and Helen M. Rara. "Strong Resolving Domination in the Lexicographic Product of Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 363–72. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4652.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. A subset S ⊆ V (G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u, v ∈ V (G), there exists a vertex w ∈ S such that u ∈ IG[v, w] or IG[u, w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G. In this paper, we characterize the strong resolving dominating sets in the lexicographic product of graphs and determine the corresponding resolving domination number.

Style APA, Harvard, Vancouver, ISO itp.

7

Mahistrado, Angelica Mae, and Helen Rara. "$1$-movable $2$-Resolving Hop Domination in Graph." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1464–79. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4770.

Pełny tekst źródła

Streszczenie:

Let $G$ be a connected graph. A set $S$ of vertices in $G$ is a 1-movable 2-resolving hop dominating set of $G$ if $S$ is a 2-resolving hop dominating set in $G$ and for every $v \in S$, either $S\backslash \{v\}$ is a 2-resolving hop dominating set of $G$ or there exists a vertex $u \in \big((V (G) \backslash S) \cap N_G(v)\big)$ such that $\big(S \backslash \{v\}\big) \cup \{u\}$ is a 2-resolving hop dominating set of $G$. The 1-movable 2-resolving hop domination number of $G$, denoted by $\gamma^{1}_{m2Rh}(G)$ is the smallest cardinality of a 1-movable 2-resolving hop dominating set of $G$. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the 1-movable 2-resolving hop dominating sets in the join, corona and lexicographic products of graphs, and determine the bounds of the 1-movable 2-resolving hop domination number of each of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

8

Sumaoy, Helyn Cosinas, and Helen M. Rara. "On Restrained Strong Resolving Domination in Graphs." European Journal of Pure and Applied Mathematics 14, no. 4 (2021): 1367–78. http://dx.doi.org/10.29020/nybg.ejpam.v14i4.4112.

Pełny tekst źródła

Streszczenie:

A set S âŠ† V (G) is a restrained strong resolving dominating set in G if S is a strongresolving dominating set in G and S = V (G) or âŸ¨V (G) \ SâŸ© has no isolated vertex. The restrained strong resolving domination number of G, denoted by Î³rsR(G), is the smallest cardinality of a restrained strong resolving dominating set in G. In this paper, we present characterizations of the restrained strong resolving dominating sets in the join, corona and lexicographic product of two graphs and determine the exact value of the restrained strong resolving domination number of each of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

9

Cabaro, Jean Mansanadez, and Helen Rara. "On 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs." European Journal of Pure and Applied Mathematics 15, no. 3 (2022): 1417–25. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4426.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A 2-resolving set S ⊆ V (G) which isdominating is called a 2-resolving dominating set or simply 2R-dominating set in G. The minimum cardinality of a 2-resolving dominating set in G, denoted by γ2R(G), is called the 2R-domination number of G. Any 2R-dominating set of cardinality γ2R(G) is then referred to as a γ2R-set in G. This study deals with the concept of 2-resolving dominating set of a graph. It characterizes the 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the 2-resolving dominating number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

10

Mahistrado, Angelica Mae, and Helen Rara. "Outer-Connected 2-Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 2 (2023): 1180–95. http://dx.doi.org/10.29020/nybg.ejpam.v16i2.4771.

Pełny tekst źródła

Streszczenie:

. Let G be a connected graph. A set S ⊆ V (G) is an outer-connected 2-resolving hop dominating set of G if S is a 2-resolving hop dominating set of G and S = V (G) or the subgraph ⟨V (G)\S⟩ induced by V (G)\S is connected. The outer-connected 2-resolving hop domination number of G, denoted by γ^c2Rh(G) is the smallest cardinality of an outer-connected 2-resolving hop dominating set of G. This study aims to combine the concept of outer-connected hop domination with the 2-resolving hop dominating sets of graphs. The main results generated in this study include the characterization of outer-connected 2-resolving hop dominating sets in the join, corona, edge corona and lexicographic product of graphs, as well as their corresponding bounds or exact values.

Style APA, Harvard, Vancouver, ISO itp.

11

Monsanto, Gerald Bacon, Penelyn L. Acal, and Helen M. Rara. "On Strong Resolving Domination in the Join and Corona of Graphs." European Journal of Pure and Applied Mathematics 13, no. 1 (2020): 170–79. http://dx.doi.org/10.29020/nybg.ejpam.v13i1.3625.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. A subset S \subseteq V(G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u,v \in V(G), there exists a vertex w \in S such that u \in I_G[v,w] or v \in I_G[u,w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G. In this paper, we characterize the strong resolving dominating sets in the join and corona of graphs and determine the bounds or exact values of the strong resolving domination number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

12

Monsanto, Gerald Bacon, Penelyn L. Acal, and Helen M. Rara. "On Strong Resolving Domination in the Join and Corona of Graphs." European Journal of Pure and Applied Mathematics 13, no. 1 (2020): 170–79. http://dx.doi.org/10.29020/nybg.ejpam.v1i1.3625.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. A subset S \subseteq V(G) is a strong resolving dominating set of G if S is a dominating set and for every pair of vertices u,v \in V(G), there exists a vertex w \in S such that u \in I_G[v,w] or v \in I_G[u,w]. The smallest cardinality of a strong resolving dominating set of G is called the strong resolving domination number of G. In this paper, we characterize the strong resolving dominating sets in the join and corona of graphs and determine the bounds or exact values of the strong resolving domination number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

13

Mahistrado, Angelica Mae, and Helen Rara. "Restrained 2-Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 286–303. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4665.

Pełny tekst źródła

Streszczenie:

    Let G be a connected graph. A set S ⊆ V (G) is a restrained 2-resolving hop dominating set of G if S is a 2-resolving hop dominating set of G and S = V (G) or ⟨V (G)\S⟩ has no isolated vertex. The restrained 2-resolving hop domination number of G, denoted by γr2Rh(G) is the smallest cardinality of a restrained 2-resolving hop dominating set of G. This study aims to combine the concept of hop domination with the restrained 2-resolving sets of graphs. The main results generated in this study include the characterization of restrained 2-resolving hop dominating sets in the join, corona, edge corona and lexicographic product of graphs, as well as their corresponding bounds or exact values.   

Style APA, Harvard, Vancouver, ISO itp.

14

Abragan, Armalene, and Helen M. Rara. "On 1-movable Strong Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 2 (2023): 763–72. http://dx.doi.org/10.29020/nybg.ejpam.v16i2.4658.

Pełny tekst źródła

Streszczenie:

A set S is a 1-movable strong resolving hop dominating set of G if for every v ∈ S, either S\{v} is a strong resolving hop dominating set or there exists a vertex u ∈ (V (G)\S)∩NG(v) such that (S \ {v}) ∩ {u} is a strong resolving hop dominating set of G. The minimum cardinality of a 1-movable strong resolving hop dominating set of G is denoted by γ 1 msRh(G). In this paper, we obtained the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the 1-movable strong resolving hop dominating sets in these types of graphs and determine the bounds or exact values of their 1-movable strong resolving hop domination numbers.

Style APA, Harvard, Vancouver, ISO itp.

15

Hausawi, Yasser M., Zaid Alzaid, Olayan Alharbi, Badr Almutairi, and Basma Mohamed. "COMPUTING THE SECURE CONNECTED DOMINANT METRIC DIMENSION PROBLEM OF CLASSES OF GRAPHS." Advances and Applications in Discrete Mathematics 42, no. 3 (2025): 219–33. https://doi.org/10.17654/0974165825015.

Pełny tekst źródła

Streszczenie:

This paper investigates the NP-hard problem of finding the lowest secure connected domination metric dimension of graphs. If each vertex in can be uniquely recognized by its vector of distances to the vertices in Scddim, then every vertex set Scddim of a connected graph resolves . If the subgraph induced by Scddim is a nontrivial connected subgraph of , then the resolving set Scddim of is connected. That resolving set is dominating if each vertex in that is not an element of Scddim is a neighbor of some vertices in Scddim. If there is a in such that is a dominating set for any in , then the dominating set is secure. If for every , there exists such that is a resolving set, then the resolving set is secure. These four cardinality values are the metric dimension of , the connected metric dimension of , the secure metric dimension of , and the connected domination metric dimension of , respectively. They correspond to the cardinality of the smallest resolving set of , the minimal connected resolving set, the minimal secure resolving set, and the minimal connected domination resolving set. In this paper, we introduce the secure connected domination metric dimension of graphs. If each vertex in G can be uniquely recognized by its vector of distances to the vertices in Scddim, then every vertex set Scddim of a connected graph resolves G. If the subgraph induced by Scddim is a nontrivial connected subgraph of G, then the resolving set Scddim of G is connected. That resolving set is dominating if each vertex in G that is not an element of Scddim is a neighbor of some vertices in Scddim. If there is a v in D such that is a dominating set for any in then the dominating set is secure. If for every there exists such that is a resolving set, then the resolving set is secure. These four cardinality values are the metric dimension of $G$, the connected metric dimension of , the secure metric dimension of , and the connected domination metric dimension of G, respectively. They correspond to the cardinality of the smallest resolving set of , the minimal connected resolving set, the minimal secure resolving set, and the minimal connected domination resolving set. In this paper, we introduce the secure connected dominant metric dimension of some graphs such as triangular snake graph, path graph, star tree and alternate quadrilateral snake. In particular, we derive the explicit formulas for the subdivision of triangular snake graph, alternate triangular snake graph, total graph of cycle graph and bistar tree.

Style APA, Harvard, Vancouver, ISO itp.

16

Alfarisi, Ridho, Dafik, and Arika Indah Kristiana. "Resolving domination number of graphs." Discrete Mathematics, Algorithms and Applications 11, no. 06 (2019): 1950071. http://dx.doi.org/10.1142/s179383091950071x.

Pełny tekst źródła

Streszczenie:

For a set [Formula: see text] of vertices of a graph [Formula: see text], the representation multiset of a vertex [Formula: see text] of [Formula: see text] with respect to [Formula: see text] is [Formula: see text], where [Formula: see text] is a distance between of the vertex [Formula: see text] and the vertices in [Formula: see text] together with their multiplicities. The set [Formula: see text] is a resolving set of [Formula: see text] if [Formula: see text] for every pair [Formula: see text] of distinct vertices of [Formula: see text]. The minimum resolving set [Formula: see text] is a multiset basis of [Formula: see text]. If [Formula: see text] has a multiset basis, then its cardinality is called multiset dimension, denoted by [Formula: see text]. A set [Formula: see text] of vertices in [Formula: see text] is a dominating set for [Formula: see text] if every vertex of [Formula: see text] that is not in [Formula: see text] is adjacent to some vertex of [Formula: see text]. The minimum cardinality of the dominating set is a domination number, denoted by [Formula: see text]. A vertex set of some vertices in [Formula: see text] that is both resolving and dominating set is a resolving dominating set. The minimum cardinality of resolving dominating set is called resolving domination number, denoted by [Formula: see text]. In our paper, we investigate and establish sharp bounds of the resolving domination number of [Formula: see text] and determine the exact value of some family graphs.

Style APA, Harvard, Vancouver, ISO itp.

17

Mohamad, Jerson Saguin, and Helen M. Rara. "On Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 14, no. 3 (2021): 1015–23. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.4055.

Pełny tekst źródła

Streszczenie:

A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v âˆˆ V (G) \ S there exists u âˆˆ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the resolving hop domination number of G. This paper presents the characterizations of the resolving hop dominating sets in the join, corona and lexicographic product of two graphs and determines the exact values of their corresponding resolving hop domination number.

Style APA, Harvard, Vancouver, ISO itp.

18

Monsanto, Gerald Bacon, and Helan Rara. "Resolving Domination in Graphs under Some Binary Operations." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 18–28. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4643.

Pełny tekst źródła

Streszczenie:

In this paper, we investigate the concept of resolving dominating set in a graph. In particular, we characterize the resolving dominating sets in the join, corona and lexicographic product of two graphs and determine the resolving domination number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

19

Subramanian, Hemalathaa, and Subramanian Arasappan. "Secure Resolving Sets in a Graph." Symmetry 10, no. 10 (2018): 439. http://dx.doi.org/10.3390/sym10100439.

Pełny tekst źródła

Streszczenie:

Let G = (V, E) be a simple, finite, and connected graph. A subset S = {u1, u2, …, uk} of V(G) is called a resolving set (locating set) if for any x ∈ V(G), the code of x with respect to S that is denoted by CS (x), which is defined as CS (x) = (d(u1, x), d(u2, x), .., d(uk, x)), is different for different x. The minimum cardinality of a resolving set is called the dimension of G and is denoted by dim(G). A security concept was introduced in domination. A subset D of V(G) is called a dominating set of G if for any v in V – D, there exists u in D such that u and v are adjacent. A dominating set D is secure if for any u in V – D, there exists v in D such that (D – {v}) ∪ {u} is a dominating set. A resolving set R is secure if for any s ∈ V – R, there exists r ∈ R such that (R – {r}) ∪ {s} is a resolving set. The secure resolving domination number is defined, and its value is found for several classes of graphs. The characterization of graphs with specific secure resolving domination number is also done.

Style APA, Harvard, Vancouver, ISO itp.

20

Mahistrado, Angelica Mae, and Helen Rara. "On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1982–97. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4585.

Pełny tekst źródła

Streszczenie:

    Let G be a connected graph. A set S of vertices in G is a 2-resolving hop dominating set of G if S is a 2-resolving set in G and for every vertex x ∈ V (G)\S there exists y ∈ S such that dG(x, y) = 2. The minimum cardinality of a set S is called the 2-resolving hop domination number of G and is denoted by γ2Rh(G). This study aims to combine the concept of hop domination with the 2-resolving sets of graphs. The main results generated in this study include the characterization of 2-resolving hop dominating sets in the join, corona and lexicographic product of two graphs, as well as their corresponding bounds or exact values.   

Style APA, Harvard, Vancouver, ISO itp.

21

Abragan, Armalene, and Helen Rara. "Restrained Strong Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1472–81. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4484.

Pełny tekst źródła

Streszczenie:

A set S ⊆ V (G) is a restrained strong resolving hop dominating set in G if for every v ∈ V (G)\S, there exists w ∈ S such that dG(v, w) = 2 and S = V (G) or V (G)\S has no isolated vertex. The smallest cardinality of such a set, denoted by γrsRh(G), is called the restrained strong resolving hop domination number of G. In this paper, we obtained the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the restrained strong resolving hop dominating sets in these types of graphs and determine the bounds or exact values of their restrained strong resolving hop domination numbers.

Style APA, Harvard, Vancouver, ISO itp.

22

Mohamad, Jerson, and Helen Rara. "Strong Resolving Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 131–43. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4578.

Pełny tekst źródła

Streszczenie:

A vertex w in a connected graph G strongly resolves two distinct vertices u and v in V (G) if v is in any shortest u-w path or if u is in any shortest v-w path. A set W of vertices in G is a strong resolving set G if every two vertices of G are strongly resolved by some vertex of W. A set S subset of V (G) is a strong resolving hop dominating set of G if S is a strong resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the strong resolving hop domination number of G. This paper presents the characterization of the strong resolving hop dominating sets in the join, corona and lexicographic product of graphs. Furthermore, this paper determines the exact value or bounds of their corresponding strong resolving hop domination number.

Style APA, Harvard, Vancouver, ISO itp.

23

Sherra, John, and Badekara Sooryanarayana. "Unique Metro Domination of a Ladder." Mapana - Journal of Sciences 15, no. 3 (2016): 55–64. http://dx.doi.org/10.12723/mjs.38.6.

Pełny tekst źródła

Streszczenie:

A dominating set $D$ of a graph $G$ which is also a resolving set of $G$ is called a metro dominating set. A metro dominating set $D$ of a graph $G(V,E)$ is a unique metro dominating set (in short an UMD-set) if $|N(v) \cap D| = 1$ for each vertex $v\in V-D$ and the minimum cardinality of an UMD-set of $G$ is the unique metro domination number of $G$. In this paper, we determine unique metro domination number of $P_n\times P_2$.

Style APA, Harvard, Vancouver, ISO itp.

24

Prihandini, Rafiantika Megahniah, Nabilah Ayu Az-Zahra, Dafik, Antonius Cahya Prihandoko, and Robiatul Adawiyah. "Resolving Independent Dominating Set pada Graf Bunga, Graf Gear, dan Graf Bunga Matahari." Contemporary Mathematics and Applications (ConMathA) 5, no. 2 (2023): 64–78. http://dx.doi.org/10.20473/conmatha.v5i2.47046.

Pełny tekst źródła

Streszczenie:

Resolving independent dominating set is the development of metric dimension and independent dominating set. Resolving independent dominating sets is a concept which discusses about determining the minimum vertex on a graph provided that the vertex that becomes the dominating set can dominate the surrounding vertex and there are no two adjacent vertices dominator and also meet the requirement of metric dimension where each vertex in graph G must have a different representation which respect to the resolving independent dominating set . In this study, we examined the resolving independent dominating set of flower graphs, gear graphs, and sunflower graphs.

Style APA, Harvard, Vancouver, ISO itp.

25

Kusumawardani, I., Dafik, E. Y. Kurniawati, I. H. Agustin, and R. Alfarisi. "On resolving efficient domination number of path and comb product of special graph." Journal of Physics: Conference Series 2157, no. 1 (2022): 012012. http://dx.doi.org/10.1088/1742-6596/2157/1/012012.

Pełny tekst źródła

Streszczenie:

Abstract We use finite, connected, and undirected graph denoted by G. Let V (G) and E(G) be a vertex set and edge set respectively. A subset D of V (G) is an efficient dominating set of graph G if each vertex in G is either in D or adjoining to a vertex in D. A subset W of V (G) is a resolving set of G if any vertex in G is differently distinguished by its representation respect of every vertex in an ordered set W. Let W = {w 1, w 2, w 3, …, wk } be a subset of V (G). The representation of vertex υ ∈ G in respect of an ordered set W is r(υ|W) = (d(υ, w 1),d(υ, w 2), …, d(υ, wk )). The set W is called a resolving set of G if r(u|W) ≠ r(υ|W) ∀ u, υ ∈ G. A subset Z of V (G) is called the resolving efficient dominating set of graph G if it is an efficient dominating set and r(u|Z) ≠ r(υ|Z) ∀ u, υ ∈ G. Suppose γre (G) denotes the minimum cardinality of the resolving efficient dominating set. In other word we call a resolving efficient domination number of graphs. We obtained γreG of some comb product graphs in this paper, namely Pm ⊲ Pn , Sm ⊲ Pn , and Km ⊲ Pn .

Style APA, Harvard, Vancouver, ISO itp.

26

Alfarisi, Ridho, Sharifah Kartini Said Husain, Liliek Susilowati, and Arika Indah Kristiana. "Dominant Mixed Metric Dimension of Graph." Statistics, Optimization & Information Computing 12, no. 6 (2024): 1826–33. http://dx.doi.org/10.19139/soic-2310-5070-1925.

Pełny tekst źródła

Streszczenie:

For $k-$ordered set $W=\{s_1, s_2,\dots, s_k \}$ of vertex set $G$, the representation of a vertex or edge $a$ of $G$ with respect to $W$ is $r(a|W)=(d(a,s_1), d(a,s_2),\dots, d(a,s_k))$ where $a$ is vertex so that $d(a,s_i)$ is a distance between of the vertex $v$ and the vertices in $W$ and $a=uv$ is edge so that $d(a,s_i)=min\{d(u,s_i),d(v,s_i)\}$. The set $W$ is a mixed resolving set of $G$ if $r(a|W)\neq r(b|W)$ for every pair $a,b$ of distinct vertices or edge of $G$. The minimum mixed resolving set $W$ is a mixed basis of $G$. If $G$ has a mixed basis, then its cardinality is called mixed metric dimension, denoted by $dim_m(G)$. A set $W$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $W$ is adjacent to some vertex of $W$. The minimum cardinality of dominating set is domination number , denoted by $\gamma(G)$. A vertex set of some vertices in $G$ that is both mixed resolving and dominating set is a mixed resolving dominating set. The minimum cardinality of mixed resolving dominating set is called dominant mixed metric dimension, denoted by $\gamma_{mr}(G)$. In our paper, we will investigated the establish sharp bounds of the dominant mixed metric dimension of $G$ and determine the exact value of some family graphs.

Style APA, Harvard, Vancouver, ISO itp.

27

Vasuki, Manimozhi, Ramachandramoorthi Shanmugapriya, Miroslav Mahdal, and Robert Cep. "A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory." Mathematics 11, no. 2 (2023): 317. http://dx.doi.org/10.3390/math11020317.

Pełny tekst źródła

Streszczenie:

Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u1, σ(u1)), (u2, σ(u2)), ...(uk, σ(uk))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements of σ − H do not have any distinct representation with regard to H, then this subset is called a fuzzy resolving set (FRS) and the smallest cardinality of this set is known as a fuzzy resolving number (FRN) and it is denoted by Fr(G). Similarly, consider a subset S such that for any u∈S, ∃v∈V − S, then S is called a fuzzy dominating set only if u is a strong arc. Now, again consider a subset F which is both a resolving and dominating set, then it is called a fuzzy resolving domination set (FRDS) and the smallest cardinality of this set is known as the fuzzy resolving domination number (FRDN) and it is denoted by Fγr(G) We have defined a few basic properties and theorems based on this FRDN and also developed an application for social network connection. Moreover, a few related statements and illustrations are discussed in order to strengthen the concept.

Style APA, Harvard, Vancouver, ISO itp.

28

Ervani, R. S. R., Dafik, I. M. Tirta, R. Alfarisi, and R. Adawiyah. "On resolving total dominating set of sunlet graphs." Journal of Physics: Conference Series 1832, no. 1 (2021): 012020. http://dx.doi.org/10.1088/1742-6596/1832/1/012020.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

29

Umilasari, Reni, Liliek Susilowati, S. Slamin, and Savari Prabhu. "On the Dominant Local Resolving Set of Vertex Amalgamation Graphs." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 4 (2023): 597–607. http://dx.doi.org/10.18860/ca.v7i4.18891.

Pełny tekst źródła

Streszczenie:

Basically, the new topic of the dominant local metric dimension which be symbolized by Ddim_l (H) is a combination of two concepts in graph theory, they were called the local metric dimension and dominating set. There are some terms in this topic that is dominant local resolving set and dominant local basis. An ordered subset W_l is said a dominant local resolving set of G if W_l is dominating set and also local resolving set of G. While dominant local basis is a dominant local resolving set with minimum cardinality. This study uses literature study method by observing the local metric dimension and dominating number before detecting the dominant local metric dimension of the graphs. After obtaining some new results, the purpose of this research is how the dominant local metric dimension of vertex amalgamation product graphs. Some special graphs that be used are star, friendship, complete graph and complete bipartite graph. Based on all observation results, it can be said that the dominant local metric dimension for any vertex amalgamation product graph depends on the dominant local metric dimension of the copied graphs and how the terminal vertex is constructed

Style APA, Harvard, Vancouver, ISO itp.

30

Mohamed, Basma, Linda Mohaisen, and Mohamed Amin. "Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem." Scientific Programming 2022 (October 6, 2022): 1–15. http://dx.doi.org/10.1155/2022/6076369.

Pełny tekst źródła

Streszczenie:

We consider, in this paper, the NP-hard problem of finding the minimum connected domination metric dimension of graphs. A vertex set B of a connected graph G = (V, E) resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set B of G is connected if the subgraph B ¯ induced by B is a nontrivial connected subgraph of G. A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B. The cardinality of the smallest resolving set of G, the cardinality of the minimal connected resolving set, and the cardinality of the minimal connected domination resolving set are the metric dimension of G, connected metric dimension of G, and connected domination metric dimension of G, respectively. We present the first attempt to compute heuristically the minimum connected dominant resolving set of graphs by a binary version of the equilibrium optimization algorithm (BEOA). The particles of BEOA are binary-encoded and used to represent which one of the vertices of the graph belongs to the connected domination resolving set. The feasibility is enforced by repairing particles such that an additional vertex generated from vertices of G is added to B, and this repairing process is iterated until B becomes the connected domination resolving set. The proposed BEOA is tested using graph results that are computed theoretically and compared to competitive algorithms. Computational results and their analysis show that BEOA outperforms the binary Grey Wolf Optimizer (BGWO), the binary Particle Swarm Optimizer (BPSO), the binary Whale Optimizer (BWO), the binary Slime Mould Optimizer (BSMO), the binary Grasshopper Optimizer (BGO), the binary Artificial Ecosystem Optimizer (BAEO), and the binary Elephant Herding Optimizer (BEHO).

Style APA, Harvard, Vancouver, ISO itp.

31

Retnowardani, Dwi Agustin, Liliek Susilowati, Dafik, and Kamal Dliou. "Distance k-domination and k-resolving domination of the corona product of graphs." Statistics, Optimization & Information Computing 13, no. 1 (2024): 72–87. https://doi.org/10.19139/soic-2310-5070-2101.

Pełny tekst źródła

Streszczenie:

For two simple graphs $G$ and $H$, the corona product of $G$ and $H$ is the graph obtained by adding a copy of $H$ for every vertex of $G$ and joining each vertex of $G$ to its corresponding copy of $H$. For $k \geq 1$, a set of vertices $D$ in a graph $G$ is a distance $k$-dominating set if any vertex in $G$ is at a distance less or equal to $k$ from some vertex in $D$. The minimum cardinality overall distance $k$-dominating sets of $G$ is the distance $k$-domination number, denoted by $\gamma_k(G)$. The metric dimension of a graph is the smallest number of vertices required to distinguish all other vertices based on distances uniquely. The distance $k$-resolving domination in graphs combines distance $k$-domination and the metric dimension of graphs. In this paper, we investigate for all $k\geq 1$, the distance $k$-domination and the distance $k$-resolving domination in the corona product of graphs. First, we show that for $k\geq 2$ the distance $k$-domination number of $G\odot H$ is equal to $\gamma_{k-1}(G)$ for any two graphs $G$ and $H$. Then, we give the exact value of $\gamma_{k}(G\odot H)$ when $G$ is a complete graph, complete $m$-partite graph, path and cycle. We also provide general bounds for $\gamma_{k}(G\odot H)$. Then, we examine the distance $k$-resolving domination number for $G\odot H$. For $k=1$, we give bounds for $\gamma^r(G\odot H)$ the resolving domination number of $G\odot H$ and characterize the graphs achieving those bounds. Later, for $k\geq 2$, we establish bounds for $\gamma^r_k(G\odot H)$ the distance $k$-resolving domination number of $G\odot H$ and characterize the graphs achieving these bounds.

Style APA, Harvard, Vancouver, ISO itp.

32

Umilasari, Reni, Liliek Susilowati, Slamin, AFadekemi Janet Osaye, and Ilham Saifudin. "Some Properties of Dominant Local Metric Dimension." Statistics, Optimization & Information Computing 12, no. 6 (2024): 1912–20. http://dx.doi.org/10.19139/soic-2310-5070-2062.

Pełny tekst źródła

Streszczenie:

Let $G$ be a connected graph with vertex set $V$. Let $W_l$ be an ordered subset defined by $W_l=\{w_1,w_2,\dots,w_n\}\subseteq V(G)$. Then $W_l$ is said to be a dominant local resolving set of $G$ if $W_l$ is a local resolving set as well as a dominating set of $G$. A dominant local resolving set of $G$ with minimum cardinality is called the dominant local basis of $G$. The cardinality of the dominant local basis of $G$ is called the dominant local metric dimension of $G$ and is denoted by $Ddim_l(G)$. We characterize the dominant local metric dimension for any graph $G$ and for some commonly known graphs in terms of their domination number to get some properties of dominant local metric dimension.

Style APA, Harvard, Vancouver, ISO itp.

33

Dapena, Adriana, Daniel Iglesia, Francisco J. Vazquez-Araujo, and Paula M. Castro. "New Computation of Resolving Connected Dominating Sets in Weighted Networks." Entropy 21, no. 12 (2019): 1174. http://dx.doi.org/10.3390/e21121174.

Pełny tekst źródła

Streszczenie:

In this paper we focus on the issue related to finding the resolving connected dominating sets (RCDSs) of a graph, denoted by G. The connected dominating set (CDS) is a connected subset of vertices of G selected to guarantee that all vertices in the graph are connected to vertices in the CDS. The connected dominating set with minimum cardinality, or minimum CDS (MCDS), is an adequate virtual backbone for information interchange in a network. When distinct vertices of G have also distinct representations with respect to a subset of vertices in the MCDS, it is said that the MCDS includes a resolving set (RS) of G. With this work, we explore different strategies to find the RCDS with minimum cardinality in complex networks where the vertices have different importances.

Style APA, Harvard, Vancouver, ISO itp.

34

Prihandini, R. M., M. R. Rahmadani, and Dafik Dafik. "ANALYSIS OF RESOLVING EFFICIENT DOMINATING SET AND ITS APPLICATION SCHEME IN SOLVING ETLE PROBLEMS." BAREKENG: Jurnal Ilmu Matematika dan Terapan 18, no. 3 (2024): 1615–28. http://dx.doi.org/10.30598/barekengvol18iss3pp1615-1628.

Pełny tekst źródła

Streszczenie:

This research focuses on the analysis of Resolving Efficient Dominating Set (REDS) and its application in solving Electronic Traffic Law Enforcement (ETLE) problems using the Spatial Temporal Graph Neural Network (STGNN). Resolving Efficient Dominating Set (REDS) is a concept in graph theory that studies a set of points in a graph that efficiently monitors other points. It involves ensuring that each point v ∈ V (G) - D is dominated by exactly one point in D, with no adjacent points in D, and the representation of point v ∈ V (G) concerning D is not the same, which is termed as a resolving efficient dominating set. In the context of Electronic Traffic Law Enforcement (ETLE), the analysis of REDS has a significant impact. The theorem resulting from the analysis of REDS enables the determination of the number of traffic violation sensors required. Furthermore, by taking simulation data from road points, violation forecasting can be performed. The accurate predictions from this forecasting can assist authorities in anticipating and addressing traffic violation issues more effectively.

Style APA, Harvard, Vancouver, ISO itp.

35

Shi, Xiaolong, Maryam Akhoundi, A. A. Talebi, and Masome Mojahedfar. "A Study on Regular Domination in Vague Graphs with Application." Advances in Mathematical Physics 2023 (May 20, 2023): 1–9. http://dx.doi.org/10.1155/2023/7098134.

Pełny tekst źródła

Streszczenie:

Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph G ∗ = X , E is a subset S of the vertices X such that every vertex not in S is adjacent to at least one member of S . The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of ϵ 1 , ϵ 2 , 2 -Regular vague dominating set and provide some examples to explain various concepts introduced. Also, some results were discussed. Additionally, the ϵ 1 , ϵ 2 , 2 -Regular strong (weak) and independent strong (weak) domination sets for vague domination set (VDS) were presented with some theorems to support the context.

Style APA, Harvard, Vancouver, ISO itp.

36

Wang, Xiaoding, Li Xu, Shuming Zhou, and Joseph Liu. "A Resolving Set based Algorithm for Fault Identification in Wireless Mesh Networks." JUCS - Journal of Universal Computer Science 21, no. (3) (2015): 384–405. https://doi.org/10.3217/jucs-021-03-0384.

Pełny tekst źródła

Streszczenie:

Abstract: Wireless Mesh Networks (WMNs) have emerged as a key technology for next-generation wireless networking. By adding some Long-ranged Links, a wireless mesh network turns into a complex network with the characteristic of small worlds. As a communication backbone, the high fault tolerance is a significant property in communication of WMNs. In this paper, we design a novel malfunctioned router detection algorithm, denoted by A-SRS, on searching resolving set based on private neighbor of dominating set. The A-SRS not only offers a highly efficient solution to position malfunctioned routers against intermitted communication that guarantees the availability of network services, but also pursues the minimum number of detecting routers due to limited resource of wireless mesh routers. We also explore the cardinality of resolving set and complexity of A-SRS based on the parameters: the minimum degree, the size of underlying graph G and the number of iterations. The algorithm enjoys better simulation results that it employs less detecting routers than the other strategies in the size of resolving set.

Style APA, Harvard, Vancouver, ISO itp.

37

Cabaro, Jean Mansanadez, and Helen Rara. "Restrained 2-Resolving Sets in the Join, Corona and Lexicographic Product of Two Graphs." European Journal of Pure and Applied Mathematics 15, no. 3 (2022): 1229–36. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4427.

Pełny tekst źródła

Streszczenie:

Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A set S ⊆ V (G) is a restrained 2-resolving set in G if S is a 2-resolving set in G and S = V (G) or ⟨V (G)\S⟩ has no isolated vertex. The restrained 2-resolving number of G, denoted by rdim2(G), is the smallest cardinality of a restrained 2-resolving set in G. A restrained 2-resolving set of cardinality rdim2(G) is then referred to as an rdim2-set in G. This study deals with the concept of restrained 2-resolving set of a graph. Itcharacterizes the restrained 2-resolving set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the 2-resolving dominating number of these graphs.

Style APA, Harvard, Vancouver, ISO itp.

38

Rao, Yongsheng, Ruiqi Cai, Ali Asghar Talebi, and Masomeh Mojahedfar. "Some Properties of Double Domination in Vague Graphs with an Application." Symmetry 15, no. 5 (2023): 1003. http://dx.doi.org/10.3390/sym15051003.

Pełny tekst źródła

Streszczenie:

This paper is devoted to the study of the double domination in vague graphs, and it is a contribution to the Special Issue “Advances in graph theory and Symmetry/Asymmetry” of Symmetry. Symmetry is one of the most important criteria that illustrate the structure and properties of fuzzy graphs. It has many applications in dominating sets and helps find a suitable place for construction. Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In the graph theory, a dominating set (DS) for a graph G*=(X,E) is a subset D of the vertices X so that every vertex which is not in D is adjacent to at least one member of D. The subject of energy in graph theory is one of the most attractive topics serving a very important role in biological and chemical sciences. Hence, in this work, we express the notion of energy on a dominating vague graph (DVG) and also use the concept of energy in modeling problems related to DVGs. Moreover, we introduce a new notion of a double dominating vague graph (DDVG) and provide some examples to explain various concepts introduced. Finally, we present an application of energy on DVGs.

Style APA, Harvard, Vancouver, ISO itp.

39

Dliou, Kamal, Adinda Putri Aziza, Dafik Dafik, Arika Indah Kristiana, and Dwi Agustin Retnowardani. "Analysis of Resolving Efficient Dominating Set and Its Application Scheme in Multi-Step Time Series Forecasting of pH and Soil Moisture in Horizontal Farming." CAUCHY: Jurnal Matematika Murni dan Aplikasi 10, no. 1 (2025): 106–16. https://doi.org/10.18860/cauchy.v10i1.29960.

Pełny tekst źródła

Streszczenie:

This research focuses on the analyzing the Resolving Efficient Dominating Set (REDS) and its application scheme in horizontal farming using the Spatial Temporal Graph Neural Network (STGNN). Soil moisture and pH are crucial factors that affect the growth and yield, as they directly impact productivity and plant health. In cases where soil moisture and pH are lacking, various types of companion planting need to be watered. In such planting systems, a central role is needed to monitor soil moisture and pH levels effectively. The placement of operators in this system requires the application of mathematical concepts, specifically graph theory. In this study, we explore graph theory, particularly the Resolving Efficient Dominating Set. This involves ensuring that each vertex is dominated by exactly one vertex in D, with no adjacent with another vertex, and the representation of vertex concerning is not the same. To effectively address this issue, including soil moisture and pH data, is required to predict future soil moisture and pH values in companion farming. Spatial Temporal Graph Neural Network (STGNN) technique proves to be useful in solving the problem of soil moisture and pH by understanding and modeling multi-step time series data. This technique aids in effectively managing and optimizing horizontal farming.

Style APA, Harvard, Vancouver, ISO itp.

40

S. Anitha and A. Francina Shalini. "Similarity Measure of Plithogenic Cubic Vague Sets: Examples and Possibilities." Neutrosophic Systems with Applications 11 (October 21, 2023): 39–47. http://dx.doi.org/10.61356/j.nswa.2023.81.

Pełny tekst źródła

Streszczenie:

The crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets are the extension of the plithogenic set, in which elements are characterized by the number of attributes and each attribute can assume many values. To achieve more accuracy and precise exclusion, a contradiction or dissimilarity degree is specified between each attribute and the values of the dominating attribute. A plithogenic cubic vague set is a combination of a plithogenic cubic set and a vague set. The key tool for resolving problems with pattern recognition and clustering analysis is the similarity measure. In this research, we characterize and investigate the similarities between two Plithogenic Cubic Vague sets (PCVSs) for (z≡F), (z≡IF) and (z≡N). Also, examples are given to examine similarities in the pattern recognition application problems.

Style APA, Harvard, Vancouver, ISO itp.

41

Yi, Eunjeong. "Bounds on the sum of broadcast domination number and strong metric dimension of graphs." Discrete Mathematics, Algorithms and Applications 12, no. 01 (2020): 2050010. http://dx.doi.org/10.1142/s179383092050010x.

Pełny tekst źródła

Streszczenie:

Let [Formula: see text] be a connected graph of order at least two with vertex set [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the length of an [Formula: see text] geodesic in [Formula: see text]. A function [Formula: see text] is called a dominating broadcast function of [Formula: see text] if, for each vertex [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text], and the broadcast domination number, [Formula: see text], of [Formula: see text] is the minimum of [Formula: see text] over all dominating broadcast functions [Formula: see text] of [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the set of vertices [Formula: see text] such that either [Formula: see text] lies on a [Formula: see text] geodesic or [Formula: see text] lies on a [Formula: see text] geodesic of [Formula: see text]. Let [Formula: see text] be a function and, for any [Formula: see text], let [Formula: see text]. We say that [Formula: see text] is a strong resolving function of [Formula: see text] if [Formula: see text] for every pair of distinct vertices [Formula: see text], and the strong metric dimension, [Formula: see text], of [Formula: see text] is the minimum of [Formula: see text] over all strong resolving functions [Formula: see text] of [Formula: see text]. For any connected graph [Formula: see text], we show that [Formula: see text]; we characterize [Formula: see text] satisfying [Formula: see text] equals two and three, respectively, and characterize unicyclic graphs achieving [Formula: see text]. For any tree [Formula: see text] of order at least three, we show that [Formula: see text], and characterize trees achieving equality. Moreover, for a tree [Formula: see text] of order [Formula: see text], we obtain the results that [Formula: see text] if [Formula: see text] is central, and that [Formula: see text] if [Formula: see text] is bicentral; in each case, we characterize trees achieving equality. We conclude this paper with some remarks and an open problem.

Style APA, Harvard, Vancouver, ISO itp.

42

Rao, Yongsheng, Saeed Kosari, Zehui Shao, Ruiqi Cai, and Liu Xinyue. "A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences." Symmetry 12, no. 11 (2020): 1885. http://dx.doi.org/10.3390/sym12111885.

Pełny tekst źródła

Streszczenie:

Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be done by applying a vague incidence graph (VIG), based on which the FGs may not engender satisfactory results. Similarly, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, and also other issues such as medical sciences, and traffic planning. Dominating sets (DSs) enjoy practical interest in several areas. In wireless networking, DSs are being used to find efficient routes with ad-hoc mobile networks. They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its important properties. In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc. Finally, a DS application for VIG to properly manage the COVID-19 testing facility is introduced.

Style APA, Harvard, Vancouver, ISO itp.

43

Muklisin, Ahmad, Arika Indah Kristiana, I. Made Tirta, and Dafik . "The development of RBL-STEM learning materials to improve the student’s forecasting thinking skills to solve resolving efficient dominating set problem." International Journal of Multidisciplinary Research and Growth Evaluation 4, no. 2 (2023): 194–99. http://dx.doi.org/10.54660/.ijmrge.2023.4.2.194-199.

Pełny tekst źródła

Streszczenie:

Forecasting thinking skills are the ability to apply the scientific method in understanding, predicting, discovering knowledge effectively problem. The Indicators of forecasting thinking skills include and identifying the solving characteristics of problems, using patterns recognition for prediction, expressing any possibility in situations that have not been observed. The thinking skills are not possed optimally by students. The aims of the research is to develop of RBL-STEM learning materials to improve the student's forecasting thinking skills to solve resolving efficient dominating set. The research shows that learning materials that have been developed must obtain valid, practical, and effective criteria. The average score for each aspect obtained on validity, criteria in this study is 3.5 for format validity, 3.6 for content validity and 3.5 for writing format validity. The score on the practicality aspect in this study is 3.8 for media format and 3.9 for language and writing on media. While the effectiveness scores in this study is 85% for student learning achievement test results, 95.5% for student activity results and 81.8% for student response results.

Style APA, Harvard, Vancouver, ISO itp.

44

Zulfatu Zainiyah, Arika Indah Kristiana, Slamin, and Dafik. "The development of RBL-STEM learning materials to improve the students’ forecasting skills in solving resolving efficient dominating set for hydroponic farming." World Journal of Advanced Research and Reviews 21, no. 1 (2024): 2233–41. http://dx.doi.org/10.30574/wjarr.2024.21.1.0217.

Pełny tekst źródła

Streszczenie:

Students' forecasting skills are currently still very low. This study aims to develop learning tools with the Riset-Based Learning (RBL) model and using the STEM (Science, Technology, Engineering, and Mathematics) approach to improve students' forecasting skills in solving resolving efficient dominating set (REDS) problems. The development of the RBL-STEM device was carried out using the 4D development model (define, design, develop, and disseminate). The developed learning tools meet valid criteria with a percentage of 92.3%, practical criteria with a percentage of 96.26%, and effective with a percentage of 89%. Based on the results of the normality test, it can be concluded that the pre-test and post-test scores are normally distributed because the p-value is higher than 0.05, namely 0.404 and 0.117. Furthermore, the paired samples T-test test produces a p-value that is less than 0.05, namely 0.000, indicating that the pretest and posttest results show that students' forecasting skills have increased statistically significant. Thus, it can be concluded that there is a significant increase in students' forecasting skills after participating in RBL-STEM learning.

Style APA, Harvard, Vancouver, ISO itp.

45

Zulfatu, Zainiyah, Indah Kristiana Arika, Slamin, and Dafik. "The development of RBL-STEM learning materials to improve the students' forecasting skills in solving resolving efficient dominating set for hydroponic farming." World Journal of Advanced Research and Reviews 21, no. 1 (2024): 2233–41. https://doi.org/10.5281/zenodo.13367299.

Pełny tekst źródła

Streszczenie:

Students' forecasting skills are currently still very low. This study aims to develop learning tools with the Riset-Based Learning (RBL) model and using the STEM (Science, Technology, Engineering, and Mathematics) approach to improve students' forecasting skills in solving resolving efficient dominating set (REDS) problems. The development of the RBL-STEM device was carried out using the 4D development model (define, design, develop, and disseminate). The developed learning tools meet valid criteria with a percentage of 92.3%, practical criteria with a percentage of 96.26%, and effective with a percentage of 89%. Based on the results of the normality test, it can be concluded that the pre-test and post-test scores are normally distributed because the p-value is higher than 0.05, namely 0.404 and 0.117. Furthermore, the paired samples T-test test produces a p-value that is less than 0.05, namely 0.000, indicating that the pretest and posttest results show that students' forecasting skills have increased statistically significant. Thus, it can be concluded that there is a significant increase in students' forecasting skills after participating in RBL-STEM learning.

Style APA, Harvard, Vancouver, ISO itp.

46

Dafik, Rasyid Ridlo Zainur, Humaizah Roizatul, Made Tirta I, and Nisviasari Rosanita. "The Analysis of the Implementation of Research-Based Learning with STEM Approach to Improving the Students' Metaliteracy in Solving the Resolving Strong Dominating Set Problem on traffic CCTV placement." International Journal of Current Science Research and Review 05, no. 08 (2022): 3106–17. https://doi.org/10.5281/zenodo.7010733.

Pełny tekst źródła

Streszczenie:

Abstract : Metaliteracy is urgently needed in the digital era, however, is still not widely owned by students. This metaliteracy requires high-level thinking skills to process various problems with various media sources, as well as it requires a collaborative environment. To achieve a good metaliteracy equipped with a higher thinking skill, we will implement research-based learning with a STEM approach in the learning process. This study uses a mixed-method by combining qualitative and quantitative methods. The subject of this study is the students of mathematics education as the candidates for teachers. They are grouped into two classes, namely, experiment class and control class. We used an independent sample t-test to determine the significant difference in the students’ metaliteracy between the experiment class and the control class under the implementation of the research-based learning model with the STEM approach to resolve the strong domination problem. Before testing the significant difference, we tested the homogeneity. The test results on the pre-test items showed that the significance score is 0.747 > 0.05, meaning the two classes are homogeneous. The independent sample t-test showed that the score is 0.020 < 0.05, which indicates that the difference between the two classes is significant. It implies that implementing the research-based learning materials with a STEM approach affects the students’ metaliteracy improvements.

Style APA, Harvard, Vancouver, ISO itp.

47

Aziza, M. O., Dafik, and A. I. Kristiana. "The analysis of the implementation of research-based learning on the students combinatorial thinking skills in solving a resolving perfect dominating set problem." Journal of Physics: Conference Series 1836, no. 1 (2021): 012057. http://dx.doi.org/10.1088/1742-6596/1836/1/012057.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

48

Hakim, R. A., Dafik, and I. M. Tirta. "The study of the implementation of research-based learning model to improve the students’ proving skills in dealing with the resolving efficient dominating set problem." Journal of Physics: Conference Series 1836, no. 1 (2021): 012059. http://dx.doi.org/10.1088/1742-6596/1836/1/012059.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

49

Muharromah M D, Kristiana A I, Slamin, and Dafik. "The development of RBL - STEM learning materials to improve students' computational thinking skills in solving convolutional neural network problems." World Journal of Advanced Research and Reviews 21, no. 1 (2024): 2373–81. http://dx.doi.org/10.30574/wjarr.2024.21.1.0219.

Pełny tekst źródła

Streszczenie:

In 21st century learning, computational thinking skills have become one of the essential competencies that need to be emphasised in the development of knowledge. To enhance computational thinking skills, research-based learning (RBL) with a science, technology, engineering and mathematics (STEM) approach, known as RBL-STEM, can be used. This study aims to explore RBL-STEM activities, describe the process and outcomes of developing RBL-STEM materials, and analyse data. In this research, the RBL-STEM framework is used to improve students' computational thinking skills in applying Convolutional Neural Network (CNN) to identify coffee plant diseases using a quadcopter drone and its flight path with resolving dominating set. The research method used is Research and Development (R&D). This research develops RBL-STEM materials and produces learning material products in the form of semester study plans, student assignment designs, student worksheets and learning outcome tests. The results of the development of the materials show validity with a validity criterion of 92%. Implementation using RBL-STEM materials was found to be practical with a practicality criterion of 96.25% and effective with an effectiveness criterion of 94.32%. In addition, students were highly engaged and provided very positive feedback on the learning experience. Pre-test and post-test analysis showed an improvement in students' computational thinking skills when solving CNN problems.

Style APA, Harvard, Vancouver, ISO itp.

50

Muharromah, M. D., A. I. Kristiana, Slamin, and Dafik. "The development of RBL - STEM learning materials to improve students' computational thinking skills in solving convolutional neural network problems." World Journal of Advanced Research and Reviews 21, no. 1 (2024): 2373–81. https://doi.org/10.5281/zenodo.13370782.

Pełny tekst źródła

Streszczenie:

In 21st century learning, computational thinking skills have become one of the essential competencies that need to be emphasised in the development of knowledge. To enhance computational thinking skills, research-based learning (RBL) with a science, technology, engineering and mathematics (STEM) approach, known as RBL-STEM, can be used. This study aims to explore RBL-STEM activities, describe the process and outcomes of developing RBL-STEM materials, and analyse data. In this research, the RBL-STEM framework is used to improve students' computational thinking skills in applying Convolutional Neural Network (CNN) to identify coffee plant diseases using a quadcopter drone and its flight path with resolving dominating set. The research method used is Research and Development (R&D). This research develops RBL-STEM materials and produces learning material products in the form of semester study plans, student assignment designs, student worksheets and learning outcome tests. The results of the development of the materials show validity with a validity criterion of 92%. Implementation using RBL-STEM materials was found to be practical with a practicality criterion of 96.25% and effective with an effectiveness criterion of 94.32%. In addition, students were highly engaged and provided very positive feedback on the learning experience. Pre-test and post-test analysis showed an improvement in students' computational thinking skills when solving CNN problems.

Style APA, Harvard, Vancouver, ISO itp.

Artykuły w czasopismach na temat „Resolving dominating set”

Utwórz poprawne odniesienie w stylach APA, MLA, Chicago, Harvard i wielu innych