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Relevant bibliographies by topics / Resolving dominating set

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Academic literature on the topic 'Resolving dominating set'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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Journal articles on the topic "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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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. 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.

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Book chapters on the topic "Resolving dominating set"

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Munawwarah, Muzayyanatun, Dafik, Arika Indah Kristiana, Elsa Yuli Kurniawati, and Rosanita Nisviasari. "On Resolving Efficient Dominating Set of Cycle and Comb Product Graph." In Proceedings of the 6th International Conference on Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022). Atlantis Press International BV, 2023. http://dx.doi.org/10.2991/978-94-6463-138-8_2.

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Muklisin, A., I. M. Tirta, Dafik, R. I. Baihaki, and A. I. Kristiana. "The Analysis of Airport Passengers Flow by Using Spatial Temporal Graph Neural Networks and Resolving Efficient Dominating Set." In Advances in Intelligent Systems Research. Atlantis Press International BV, 2023. http://dx.doi.org/10.2991/978-94-6463-174-6_2.

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London, Alex John. "A Non-Paternalistic Model of Research Ethics and Oversight." In For the Common Good. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197534830.003.0007.

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This chapter argues that prospective review of research before bodies of diverse representation should not be understood as a paternalistic interference in the private interactions between researchers and participants. Instead, it is a mechanism for resolving a set of coordination problems that threaten the integrity of research. Its proper role is to provide credible social assurance that the research enterprise constitutes a voluntary scheme of cooperation through which diverse stakeholders can contribute to the common good without being subject to the arbitrary exercise of social authority including antipathy, abuse, coercion, domination, exploitation, or other forms of harmful, unfair, or disrespectful treatment. The limitations of prospective review are discussed, including the need for mechanisms that better address incentives for a wider range of stakeholders whose decisions shape the research agenda.

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Conference papers on the topic "Resolving dominating set"

1

Zainiyah, Zulfatu, Arika Indah Kristiana, Slamin, Dafik, and Indah Lutfiyatul Mursyidah. "On time series forecasting on NPK and pH concentration of hydroponic plants by means of resolving efficient domination set of graph." In THE 7TH INTERNATIONAL CONFERENCE OF COMBINATORICS, GRAPH THEORY, AND NETWORK TOPOLOGY 2023. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0222453.

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