期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2017
卷号：14
期号：3
页码：216-223
DOI：10.1016/j.akcej.2017.03.003
语种：English
出版社：Elsevier
摘要：Abstract For any (finite simple) graph G the secure domination number of G satisfies γ s ( G ) ≥ | V ( G ) | 2 . Here we find a secure-dominating set S in G such that | S | = ⌈ | V ( G ) | 2 ⌉ in all cases when G is a grid, and in the majority of cases when G is a cylindrical or toroidal grid. In all such cases, S satisfies the additional requirement that G [ S ] is connected. We make note that the concept of secure-dominating sets considered in this paper is quite different from the other secure domination currently of interest. 1 1 The other sort of secure domination: A dominating set S ⊆ V ( G ) is secure dominating (in G) if and only if for every v ∈ V ( G ) ∖ S there is some u ∈ S such that ( S ∖ { u } ) ∪ { v } is dominating, in G.
关键词：KeywordsenSecurity in graphsDominating setsHub sets
