Results 41 to 50 of about 16,468 (299)
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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On total domination and total equitable domination in graphs
Malaya Journal of Matematik, 2018 A dominating set $D$ of a graph $G$ is called total if every vertex of $V(G)$ is adjacent to at least one vertex of $D$, equivalently if $N(D)=V(G)$ then $D$ is called total dominating set. A dominating set $D$ is called total equitable dominating set if it is total and for every vertex in $V(G)-D$ there exists a vertex in $D$ such that they are ...
null S. K. Vaidya, null A. D. Parmar
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On Roman, Global and Restrained Domination in Graphs [PDF]
, 2010 In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible.
Zverovich, Vadim +3 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, $γ_t(G)$. 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 ...
Michael A. Henning, Viroshan Naicker
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Total Dominator Colorings in Paths [PDF]
, 2012 Determining the total dominator chromatic number in ...
Vijayalekshmi, A., A. Vijayalekshmi
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Trees with equal total domination and total restrained domination numbers [PDF]
, 2008 For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number.
Shiu, Wai, Chen, Hong-Yu, Chen, Xue-Gang
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Total Domination in Partitioned Graphs [PDF]
Graphs and Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Frendrup, Allan +2 more
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Total Domination Cover Rubbling [PDF]
, 2020 Let G be a connected simple graph with vertex set V and a distribution of pebbles on the vertices of V. The total domination cover rubbling number of G is the minimum number of pebbles, so that no matter how they are distributed, it is possible that ...
Haynes, Teresa W. +3 more
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Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight
Klein Douglas J. +1 more
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Properties of the Global Total k-Domination Number
Mathematics, 2021 A nonempty subset D⊂V of vertices of a graph G=(V,E) is a dominating set if every vertex of this graph is adjacent to at least one vertex from this set except the vertices which belong to this set itself.
Frank A. Hernández Mira +3 more
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