Results 41 to 50 of about 13,369 (211)
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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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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Some notes on the isolate domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2017 A subset of vertices of a graph is a dominating set of if every vertex in has a neighbor in . The domination number is the minimum cardinality of a dominating set of . A dominating set is an isolate dominating set if the induced subgraph has at least one
Nader Jafari Rad
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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 versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2012 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by t.
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Double total domination of graphs
Discrete Mathematics, 1997 Let \(G\) be a graph with vertices \(V\) and edges \(E\). A set \(S\subset E\cup V\) is said to be a total dominating set of \(G\) if each vertex and edge of \(G\) is in \(S\), or adjacent or incident to a member of \(S\). The total domination number \(\alpha_2(G)\) is the cardinality of the smallest subset \(S\) which is a total dominating set of \(G\)
John Gimbel +2 more
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Hop total Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this article, we initiate a study of hop total Roman domination defined as follows: a hop total Roman dominating function (HTRDF) on a graph [Formula: see text] is a function [Formula: see text] such that for every vertex u with f(u) = 0 there exists ...
H. Abdollahzadeh Ahangar +3 more
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On the total Roman domination stability in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has ...
Ghazale Asemian +3 more
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On the Total k-Domination in Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets.
Bermudo Sergio +2 more
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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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