Results 61 to 70 of about 11,159 (184)
Domination parameters of a graph with added vertex [PDF]
Opuscula Mathematica, 2004 Let \(G=(V,E)\) be a graph. A subset \(D\subseteq V\) is a total dominating set of \(G\) if for every vertex \(y\in V\) there is a vertex \(x\in D\) with \(xy\in E\).
Maciej Zwierzchowski
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Total domination number of the conjunction of graphs
Discrete Mathematics, 2007 AbstractIn this paper we discuss the total domination number with respect to the conjunction of two graphs. We estimate the total domination number of the conjunction G∧H, showing that γt(G∧H)⩽γt(G)γt(H), for graphs having no isolated vertices. Additionally, we show that for G≅Pn or for G and H having the domination number equal to half their orders ...
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Total and paired domination numbers of toroidal meshes [PDF]
Journal of Combinatorial Optimization, 2012 Let $G$ be a graph without isolated vertices. The total domination number of $G$ is the minimum number of vertices that can dominate all vertices in $G$, and the paired domination number of $G$ is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching.
Jun-Ming Xu, Fu-Tao Hu
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On graphs with equal total domination and connected domination numbers
Applied Mathematics Letters, 2006 AbstractA subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt(G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected.
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Relating the annihilation number and the total domination number of a tree
Discrete Applied Mathematics, 2013 AbstractA set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is ...
Desormeaux, Wyatt J. +2 more
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Bounds on the 2-domination number in cactus graphs [PDF]
Opuscula Mathematica, 2006 A \(2\)-dominating set of a graph \(G\) is a set \(D\) of vertices of \(G\) such that every vertex not in \(S\) is dominated at least twice. The minimum cardinality of a \(2\)-dominating set of \(G\) is the \(2\)-domination number \(\gamma_{2}(G)\).
Mustapha Chellali
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Total Roman Reinforcement in Graphs
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Ahangar H. Abdollahzadeh +4 more
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Computing locating-total domination number in some rotationally symmetric graphs. [PDF]
Sci Prog, 2021 Raza H, Iqbal N, Khan H, Botmart T.
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Nordhaus–Gaddum type inequalities on the total Italian domination number in graphs [PDF]
, 2022 Seyed Mahmoud Sheikholeslami +1 more
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Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
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