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Artykuły w czasopismach na temat „Neighborhood total domination”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Hassan, Javier, and Sergio R. Canoy, Jr. "Grundy Total Hop Dominating Sequences in Graphs." European Journal of Pure and Applied Mathematics 16, no. 4 (2023): 2597–612. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4877.

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Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) \Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy

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2

Sivagnanam, C. "Neighborhood Total Domination and Colouring in Graphs." International Journal of Mathematics and Soft Computing 5, no. 1 (2015): 143. http://dx.doi.org/10.26708/ijmsc.2015.1.5.16.

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Wang, Kan, Changhong Lu, and Bing Wang. "Bounds on Neighborhood Total Domination Numberin Graphs." Bulletin of the Iranian Mathematical Society 45, no. 4 (2019): 1135–43. http://dx.doi.org/10.1007/s41980-018-0189-4.

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4

Henning, Michael A., and Nader Jafari Rad. "Bounds on neighborhood total domination in graphs." Discrete Applied Mathematics 161, no. 16-17 (2013): 2460–66. http://dx.doi.org/10.1016/j.dam.2013.05.014.

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5

Henning, Michael A., and Kirsti Wash. "Trees with large neighborhood total domination number." Discrete Applied Mathematics 187 (May 2015): 96–102. http://dx.doi.org/10.1016/j.dam.2015.01.037.

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6

RAD, NADER JAFARI. "A note on neighborhood total domination in graphs." Proceedings - Mathematical Sciences 125, no. 3 (2015): 271–76. http://dx.doi.org/10.1007/s12044-015-0241-8.

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7

Lee, Chuan-Min. "Exploring Dominating Functions and Their Complexity in Subclasses of Weighted Chordal Graphs and Bipartite Graphs." Mathematics 13, no. 3 (2025): 403. https://doi.org/10.3390/math13030403.

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Domination problems are fundamental problems in graph theory with diverse applications in optimization, network design, and computational complexity. This paper investigates {k}-domination, k-tuple domination, and their total domination variants in weighted strongly chordal graphs and chordal bipartite graphs. Specifically, the {k}-domination problem in weighted strongly chordal graphs and the total {k}-domination problem in weighted chordal bipartite graphs are shown to be solvable in O(n+m) time. For weighted proper interval graphs and convex bipartite graphs, we solve the k-tuple domination

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8

Sheikholeslami, Seyed Mahmoud, and Lutz Volkmann. "Outer independent total double Italian domination number." Computer Science Journal of Moldova 32, no. 1(94) (2024): 19–37. http://dx.doi.org/10.56415/csjm.v32.02.

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If $G$ is a graph with vertex set $V(G)$, then let $N[u]$ be the closed neighborhood of the vertex $u\in V(G)$. A total double Italian dominating function (TDIDF) on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ satisfying (i) $f(N[u])\ge 3$ for every vertex $u\in V(G)$ with $f(u)\in\{0,1\}$ and (ii) the subgraph induced by the vertices with a non-zero label has no isolated vertices. A TDIDF is an outer-independent total double Italian dominating function (OITDIDF) on $G$ if the set of vertices labeled $0$ induces an edgeless subgraph. The weight of an OITDIDF is the sum of its func

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9

Jha, Anupriya, D. Pradhan, and S. Banerjee. "Algorithm and hardness results on neighborhood total domination in graphs." Theoretical Computer Science 840 (November 2020): 16–32. http://dx.doi.org/10.1016/j.tcs.2020.05.002.

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10

Lu, Changhong, Bing Wang та Kan Wang. "Algorithm complexity of neighborhood total domination and $$(\rho ,\gamma _{nt})$$ ( ρ , γ n t ) -graphs". Journal of Combinatorial Optimization 35, № 2 (2017): 424–35. http://dx.doi.org/10.1007/s10878-017-0181-6.

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11

Arumugam, S., and K. Raja Chandrasekar. "Linear time algorithm for dominator chromatic number of trestled graphs." Discrete Mathematics, Algorithms and Applications 11, no. 06 (2019): 1950066. http://dx.doi.org/10.1142/s1793830919500666.

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A dominator coloring (respectively, total dominator coloring) of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] such that each closed neighborhood (respectively, open neighborhood) of every vertex of [Formula: see text] contains a color class of [Formula: see text] The minimum number of colors required for a dominator coloring (respectively, total dominator coloring) of [Formula: see text] is called the dominator chromatic number (respectively, total dominator chromatic number) of [Formula: see text] and is denoted by [Formula: see text] (respective

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12

Shanmugam, Megala, Mohanapriya Nagaraj, Karthika Ravichandran, and Abirami Kamaraj. "On dominator and total dominator coloring of duplication corresponding corona of path, pan, complete and sunlet graphs." Open Journal of Discrete Applied Mathematics 8, no. 2 (2025): 18–31. https://doi.org/10.30538/psrp-odam2025.0113.

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A dominator coloring of a graph \(\mathscr{G}\) is a proper coloring where each vertex of \(\mathscr{G}\) is within the closed neighborhood of at least one vertex from each color class. The minimum number of color classes required for a dominator coloring of \(\mathscr{G}\) is termed the dominator chromatic number. Additionally, a total dominator coloring of a graph \(\mathscr{G}\) is a proper coloring in which every vertex dominates at least one color class other than its own. The minimum number of color classes needed for a total dominator coloring of \(\mathscr{G}\) is known as the total do

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13

Zhang, Yameng, and Xia Zhang. "On the fractional total domatic numbers of incidence graphs." Mathematical Modelling and Control 3, no. 1 (2023): 73–79. http://dx.doi.org/10.3934/mmc.2023007.

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<abstract><p>For a hypergraph $ H $ with vertex set $ X $ and edge set $ Y $, the incidence graph of hypergraph $ H $ is a bipartite graph $ I(H) = (X, Y, E) $, where $ xy\in E $ if and only if $ x\in X $, $ y\in Y $ and $ x\in y $. A total dominating set of graph $ G $ is a vertex subset that intersects every open neighborhood of $ G $. Let $ \mathscr{M} $ be a family of (not necessarily distinct) total dominating sets of $ G $ and $ r_{\mathscr{M}} $ be the maximum times that any vertex of $ G $ appears in $ \mathscr{M} $. The fractional domatic number $ G $ is defined as $ FTD(G

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14

Iordanski, Mikhail A. "Dominant sets with neighborhood for trees." Modeling and Analysis of Information Systems 32, no. 1 (2025): 32–41. https://doi.org/10.18255/1818-1015-2025-1-32-41.

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The subset $V' \subset V(G)$ forms a dominant set of vertices of the graph $G$ with a neighborhood $ \varepsilon$ if for any vertex $v \in V \backslash V'$ there is a vertex $u \in V'$ such that the length of the shortest chain connecting these vertices $d(v,u)\leqslant \varepsilon$; $\delta_{\varepsilon}(G)$ is the number of vertices in the minimal $\varepsilon$-dominating set; $\delta_{\varepsilon}(G) = 1$ for $r(G)\leqslant \varepsilon \leqslant d(G)$; for $ \varepsilon < r(G)$ the numbers $\delta_{\varepsilon}(G) > 1$, but the calculation of $\delta_{1}(G)=\delta(G)$ is an NP-complet

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15

Sinar, T. Ricky Hafidsyah, Feby Milanie, Cut Nuraini, Abdiyanto Abdiyanto, and Ihsan Azhari. "Analysis of Determining Service Center Systems towards the Development of The Eastern Part of Medan City." International Journal Papier Advance and Scientific Review 4, no. 4 (2023): 91–105. http://dx.doi.org/10.47667/ijpasr.v4i4.258.

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The issues in the research area include a high concentration of built-up residential areas with the potential for slums and warehousing activities dominating trade and service areas or residential areas, leading to congestion. This requires attention, considering that the Eastern Part of Medan City has a high built-up area, necessitating the provision of affordable infrastructure and basic services for both newcomers and existing residents in the city. Several development theories and concepts can assist in determining and conceptualizing development in the research area. The study focuses on

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16

Dundar, Bayram. "A simulated annealing with graph-based search for the social-distancing problem in enclosed areas during pandemics." PLOS ONE 20, no. 2 (2025): e0318380. https://doi.org/10.1371/journal.pone.0318380.

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During the pandemic, decision-makers offered many preventive policies to reduce the negative effects of the pandemic. The social distance rule in enclosed areas was implemented by educational institutions in any countries. In this study, we deal with the problem of assigning students to seats by considering the social distancing constraint and with objective of maximizing the total distance among the students. This problem is found to be similar to the Maximum Diversity Problem (MDP) in the literature. We name this new problem as Maximum Diversity Social Distancing problem (MDPs). A simulated

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17

Parpan, V. I., N. V. Shumska, M. J. Rudeichuk-Kobzeva, and M. M. Mylenka. "Syntaxonomy of vegetation of Kalush hexachlorobenzene toxic waste landfill (Ivano-Frankivsk region)." Biosystems Diversity 24, no. 2 (2016): 364–70. http://dx.doi.org/10.15421/011648.

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The vegetation of a landfill of hexachlorobenzene toxic waste was studied. It is situated in the neighborhood of Kalush (Ivano-Frankivsk region) and has an area of 4.5 ha. As a result of damage to the containers, hazardous waste has contaminated the air, soil and aquifers at the test site and adjacent areas. During the period 2010–2012 measures were taken to recover and remove the mixture of toxic waste and contaminated soil from the landfill. In its place, unpolluted soil was brought to the landfill. Work was carried out to recultivate the territory. Nowadays natural succession of vegetation

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18

Adamış, Emel, and Fatih Pınarbaşı. "Unfolding visual characteristics of social media communication: reflections of smart tourism destinations." Journal of Hospitality and Tourism Technology 13, no. 1 (2022): 34–61. http://dx.doi.org/10.1108/jhtt-09-2020-0246.

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Purpose This study aims to explore the visual social media (SM) (Instagram) communication and the visual characteristics of smart tourism destination (STD) communication from destination marketing/management organizations (DMOs) and user-generated content (UGC) perspectives, which refer to projected image and perceived image, respectively. Design/methodology/approach Three DMO official accounts of STDs (Helsinki, Gothenburg and Lyon) and corresponding official hashtags were selected for the sample and total 6,000 post data (1,000 × 6) were retrieved from Instagram. Visual communication content

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19

C.Sivagnanam. "Neighborhood Total 2-Domination in Graphs." November 30, 2014. https://doi.org/10.5281/zenodo.826659.

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The graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m respectively. For graph theoretic terminology we refer to Chartrand and Lesniak [3] and Haynes et.al [5-6].

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20

Singhwal, Nitisha, and Palagiri Venkata Subba Reddy. "Total vertex-edge domination in graphs: Complexity and algorithms." Discrete Mathematics, Algorithms and Applications, November 15, 2021. http://dx.doi.org/10.1142/s1793830922500318.

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Let [Formula: see text] be a simple, undirected and connected graph. A vertex [Formula: see text] of a simple, undirected graph [Formula: see text]-dominates all edges incident to at least one vertex in its closed neighborhood [Formula: see text]. A set [Formula: see text] of vertices is a vertex-edge dominating set of [Formula: see text], if every edge of graph [Formula: see text] is [Formula: see text]-dominated by some vertex of [Formula: see text]. A vertex-edge dominating set [Formula: see text] of [Formula: see text] is called a total vertex-edge dominating set if the induced subgraph [F

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21

Salim, Jeffrey, Glee Tampipi, Albert Quinones, and Rosalio Artes Jr. "Connected Total Domination Neighborhood Polynomials Over Distance-Reducing Operations." International Journal of Mathematics and Computer Science, 2025, 767–70. https://doi.org/10.69793/ijmcs/03.2025/salim.

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22

Foucaud, Florent, and Michael A. Henning. "Locating-Total Dominating Sets in Twin-Free Graphs: a Conjecture." Electronic Journal of Combinatorics 23, no. 3 (2016). http://dx.doi.org/10.37236/5147.

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A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. A locating-total dominating set of $G$ is a total dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \ne N(v) \cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-total domination number of $G$, denoted $\gamma_

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23

Chen, Qin. "Algorithm aspect on total Roman $\{2\}$-domination number of Cartesian products of paths and cycles." RAIRO - Operations Research, September 3, 2023. http://dx.doi.org/10.1051/ro/2023121.

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A total Roman $\{2\}$-dominating function (TR2DF) on a graph $G$ with vertex set $V$ is a function $f: V\rightarrow \{0,1,2\}$ having the property that for every vertex $v$ with $f(v)=0$, $\sum_{u\in N(v)}f(u)\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and the subgraph of $G$ induced by the set of vertices with $f(v)>0$ has no isolated vertex. The weight of a TR2DF $f$ is the value $w(f)=\sum_{v\in V} f(v)$, and the minimum weight of a TR2DF of $G$ is the total Roman $\{2\}$-domination number $\gamma_{tR2}(G)$. The total Roman $\{2\}$-domination problem (TR2DP) is to dete

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24

Mahmoodi, Akram, Maryam Atapour, and Sepideh Norouzian. "On the signed strong total Roman domination number of graphs." Tamkang Journal of Mathematics, July 29, 2022. http://dx.doi.org/10.5556/j.tkjm.54.2023.3907.

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Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ forwhich $f(v)=-1$ is adjacent to at least one vertex$w$ for which $f(w)\geq 1+\lceil\frac{1}{2}\vert N(w)\cap V_{-1}\vert\rceil$, where$V_{-1}=\{v\in V: f(v)=-1\}$.The minimum of thevalues $\omega(f)

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25

Casado, Alejandra, Jesús Sánchez-Oro, and Anna Martínez-Gavara. "Heuristics for the weighted total domination problem." TOP, February 10, 2025. https://doi.org/10.1007/s11750-025-00695-1.

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Abstract The weighted total domination problem (WTDP) belongs to the family of dominating set problems. Given an edge- and vertex- weighted graph, the WTDP consists in selecting a total dominating set D, such that the sum of vertices and edges weights of the subgraph induced by D plus, for each vertex not in D, the minimum weight of its edge to a vertex in D is minimized. A total dominating set D is a subset of the graph’s vertices, such that every vertex, including those in D, is at least adjacent to one vertex in D. This problem arises in many real-life applications closely related to coveri

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26

Shahbazi, L., H. Abdollahzadeh Ahangar, R. Khoeilar, and S. M. Sheikholeslami. "Total k-rainbow reinforcement number in graphs." Discrete Mathematics, Algorithms and Applications, September 7, 2020, 2050101. http://dx.doi.org/10.1142/s1793830920501013.

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Let [Formula: see text] be an integer, and let [Formula: see text] be a graph. A k-rainbow dominating function (or [Formula: see text]RDF) of [Formula: see text] is a function [Formula: see text] from the vertex set [Formula: see text] to the family of all subsets of [Formula: see text] such that for very [Formula: see text] with [Formula: see text], the condition [Formula: see text] is fulfilled, where [Formula: see text] is the open neighborhood of [Formula: see text]. The weight of a [Formula: see text]RDF [Formula: see text] of [Formula: see text] is the value [Formula: see text]. A k-rain

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27

Kapunac, Stefan, Aleksandar Kartelj, and Marko Djukanovic. "Variable Neighborhood Search for Weighted Total Domination Problem and its Application in Social Network Information Spreading." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4155122.

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Kapunac, Stefan, Aleksandar Kartelj, and Marko Djukanović. "Variable neighborhood search for weighted total domination problem and its application in social network information spreading." Applied Soft Computing, May 2023, 110387. http://dx.doi.org/10.1016/j.asoc.2023.110387.

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29

Artes, Rosalio G. Jr. "CONNECTED TOTAL DOMINATING NEIGHBORHOOD POLYNOMIAL OF GRAPHS." Advances and Applications in Discrete Mathematics, May 23, 2023, 145–54. http://dx.doi.org/10.17654/0974165823042.

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Artes Jr., Rosalio, Cerina Villarta, Venerando Tenio, Milani Udal, and Angelito Rendiza. "Algebraic Representation of CTDS Over Uniform Network Interactions." International Journal of Mathematics and Computer Science, 2025, 791–95. https://doi.org/10.69793/ijmcs/03.2025/avtur.

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In this paper, we characterize the connected total dominating sets (CTDS) in graphs resulting from uniform network interactions. Moreover, we establish the polynomial representation of the resulting graph with respect to its CTDS and neighborhood systems. We have shown that the polynomial can be expressed as the product of a binomial expansion and exponential form.

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