Results 31 to 40 of about 13,369 (211)
On the total domination number of total graphs
Discussiones Mathematicae Graph TheoryAbel Cabrera-Martínez +2 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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Jambura Journal of Mathematics, 2022 Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G).
Nurhamzah Nurhamzah +2 more
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Total Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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The Electronic Journal of Combinatorics, 2017 Using hypergraph transversals it is proved that $\gamma_t(Q_{n+1}) = 2\gamma(Q_n)$, where $\gamma_t(G)$ and $\gamma(G)$ denote the total domination number and the domination number of $G$, respectively, and $Q_n$ is the $n$-dimensional hypercube. More generally, it is shown that if $G$ is a bipartite graph, then $\gamma_t(G \square K_2) = 2\gamma(G ...
Jernej Azarija +2 more
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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Bounds on Global Total Domination in Graphs [PDF]
Computer Science Journal of Moldova, 2015 A subset $S$ of vertices in a graph $G$ is a \textit{global total dominating set}, or just GTDS, if $S$ is a \textit{total dominating set} of both $G$ and $\overline{G}$.
Nader Jafari Rad, Elahe Sharifi
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Trees with equal total domination and game total domination numbers
Discrete Applied Mathematics, 2017 23 pages, 5 figures, 22 ...
Michael A. Henning, Douglas F. Rall
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Total Domination in Partitioned Graphs [PDF]
Graphs and Combinatorics, 2009 Udgivelsesdato ...
Frendrup, Allan +2 more
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Disjunctive total domination in graphs [PDF]
Journal of Combinatorial Optimization, 2014 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, $ _t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $
Viroshan Naicker, Michael A. Henning
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