Results 51 to 60 of about 16,468 (299)
Equality of total domination and chromatic total domination in graphs
International journal of health sciences, 2022 Let be a simple, finite and undirected graph and without isolated vertex. A subset D of V is said to be dominating set if for every in there exist a vertex in such that and are adjacent. The minimum cardinality of a dominating set of is called the domination number of and is denoted by .
M. Angala Eswari, S. Balamurugan
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Total Domination Stable Graphs [PDF]
, 2019 In this paper, we study the total domination number and total domination polynomials of some graph and its square. We discuss nonzero real total domination roots of these graphs.
Shyama M.P., Anil Kumar V.
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Total Domination on Some Graph Operators
Mathematics, 2021 Let G=(V,E) be a graph; a set D⊆V is a total dominating set if every vertex v∈V has, at least, one neighbor in D. The total domination number γt(G) is the minimum cardinality among all total dominating sets.
José M. Sigarreta
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Total domination dot-critical graphs [PDF]
, 2011 A graph G with no isolated vertex is total domination vertex-critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G−v is less than the total domination number of G.
Rad, Nader Jafari +3 more
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Total Roman Domination Number of Rooted Product Graphs
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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Total domination and least domination in a tree
Discrete Mathematics, 2003 A subset \(X\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating (or total dominating) in \(G\), if for each \(x\in V(G)- X\) (or for each \(x\in V(G)\), respectively) there exists \(y\in X\) adjacent to \(x\). The least number of vertices of a dominating (or total dominating) set in \(G\) is the domination number \(\gamma(G)\) (or the ...
Xuezheng Lv, Jingzhong Mao
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On total restrained domination in graphs [PDF]
, 1999 summary:In this paper we initiate the study of total restrained domination in graphs. Let $G=(V,E)$ be a graph. A total restrained dominating set is a set $S\subseteq V$ where every vertex in $V-S$ is adjacent to a vertex in $S$ as well as to another ...
Renu C. Laskar +12 more
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On the Complexity of Reinforcement in Graphs
Discussiones Mathematicae Graph Theory, 2016 We show that the decision problem for p-reinforcement, p-total rein- forcement, total restrained reinforcement, and k-rainbow reinforcement are NP-hard for bipartite graphs.
Rad Nader Jafari
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On a conjecture concerning total domination subdivision number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
S. Kosari +5 more
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Total 2-Rainbow Domination in Graphs
Mathematics, 2022 A total k-rainbow dominating function on a graph G=(V,E) is a function f:V(G)→2{1,2,…,k} such that (i) ∪u∈N(v)f(u)={1,2,…,k} for every vertex v with f(v)=∅, (ii) ∪u∈N(v)f(u)≠∅ for f(v)≠∅.
Huiqin Jiang, Yongsheng Rao
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