Results 1 to 10 of about 13,369 (211)
Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 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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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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Lower Bounds for the Total Distance $k$-Domination Number of a Graph
Theory and Applications of GraphsFor $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total distance $k$-dominating set} of $G$ is a set of vertices $S \subseteq V(G)$ such that every vertex in $G$ is within distance $k$ to some vertex of $S$ other than itself.
Randy R. Davila
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Total restrained reinforcement in graphs
AKCE International Journal of Graphs and Combinatorics, 2016 In this paper we initiate the study of total restrained reinforcement in graphs. The total restrained reinforcement number in a graph G with no isolated vertex, is the minimum number of edges that have to be added to G so that the resulting graph has ...
Nader Jafari Rad, Lutz Volkmann
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Bounds On The Disjunctive Total Domination Number Of A Tree
Discussiones Mathematicae Graph Theory, 2016 Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G).
Henning Michael A., Naicker Viroshan
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Two Short Proofs on Total Domination
Discussiones Mathematicae Graph Theory, 2013 A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set.
Bickle Allan
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Bounds on weak and strong total domination in graphs
Electronic Journal of Graph Theory and Applications, 2016 A set $D$ of vertices in a graph $G=(V,E)$ is a total dominatingset if every vertex of $G$ is adjacent to some vertex in $D$. Atotal dominating set $D$ of $G$ is said to be weak if everyvertex $v\in V-D$ is adjacent to a vertex $u\in D$ such that$d_{G}(v)
M.H. Akhbari, Nader Jafari Rad
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