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Total domination number of middle graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set.
Farshad Kazemnejad +3 more
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Total and Double Total Domination Number on Hexagonal Grid [PDF]
Mathematics, 2019 In this paper, we determine the upper and lower bound for the total domination number and exact values and the upper bound for the double-total domination number on hexagonal grid H m , n with m hexagons in a row and n hexagons in a column ...
Antoaneta Klobučar, Ana Klobučar
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On a Class of Graphs with Large Total Domination Number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$.
Selim Bahadır, Didem Gözüpek
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Total Domination Multisubdivision Number of a Graph
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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On the total domination subdivision numbers in graphs [PDF]
Open Mathematics, 2010 Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
Sheikholeslami Seyed
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Total Roman Domination Number of Rooted Product Graphs [PDF]
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
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On the game total domination number [PDF]
Graphs and Combinatorics, 2017 11 ...
Csilla Bujtás
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Minimum Randić Index of Trees with Fixed Total Domination Number [PDF]
Mathematics, 2022 The Randić index is among the most famous degree-based topological indices in chemical graph theory. It was introduced due to its application in modeling the properties of certain molecular structures and has been extensively studied.
Ayu Ameliatul Shahilah Ahmad Jamri +4 more
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On the total domination number of cross products of graphs
Discrete Mathematics, 2007 We give lower and upper bounds on the total domination number of the cross product of two graphs, γ t(G×H). These bounds are in terms of the total domination number and the maximum degree of the factors and are best possible. We further investigate cross products involving paths and cycles. We determine the exact values of γ t(G×Pn) and γ
Mohamed El-Zahar +2 more
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Double total domination number in certain chemical graphs
AIMS Mathematics, 2022 Let $ G $ be a graph with the vertex set $ V(G) $. A set $ D\subseteq V(G) $ is a total k-dominating set if every vertex $ v\in V(G) $ has at least $ k $ neighbours in $ D $.
Ana Klobučar Barišić +1 more
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