END SUPER DOMINATING SETS IN GRAPHS

被引：0

作者：

Akbari, Saieed ^{[1
]}

Ghanbari, Nima ^{[2
]}

Henning, Michael A. ^{[3
]}

机构：

[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran

[2] Univ Bergen, Dept Informat, POB 7803, N-5020 Bergen, Norway

[3] Univ Johannesburg, Dept Math & Appl Math, ZA-2006 Auckland Pk, South Africa

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2023年

关键词：

domination number; end super dominating set; end super dom-ination number; networks; generalization; NUMBER;

D O I：

10.7151/dmgt.2519

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G = (V, E) be a simple graph. A dominating set of G is a subset S subset of V such that every vertex not in S is adjacent to at least one vertex in S. The cardinality of a smallest dominating set of G, denoted by gamma(G), is the domination number of G. A super dominating set is a dominating set S with the additional property that every vertex in V \ S has a neighbor in S that is adjacent to no other vertex in V \S. Moreover if every vertex in V \S has degree at least 2, then S is an end super dominating set. The end super domination number is the minimum cardinality of an end super dominating set. We give applications of end super dominating sets as main servers and temporary servers of networks. We determine the exact value of the end super domination number for specific classes of graphs, and we count the number of end super dominating sets in these graphs. Tight upper bounds on the end super domination number are established, where the graph is modified by vertex (edge) removal and contraction.

引用

页码：21 / 47

页数：27

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