Title

Global Secure Sets Of Grid-Like Graphs

Keywords

Cartesian product; Cycle; Dominating set; Grid graph; Security number

Abstract

Let G=(V,E) be a graph and S⊆V. The set S is a secure set if ∀X⊆S,|N[X]∩S|<|N[X]-S|, and S is a global secure set if S is a secure set and a dominating set. The cardinality of a minimum global secure set of G is the global security number of G, denoted γs(G). The sets studied in this paper are different from secure dominating sets studied in Cockayne et al. (2003) [3], Grobler and Mynhardt (2009) [8], or Klostermeyer and Mynhardt (2008) [13], which are also denoted by γs. In this paper, we provide results on the global security numbers of paths, cycles and their Cartesian products. © 2010 Elsevier B.V. All rights reserved.

Publication Date

3-28-2011

Publication Title

Discrete Applied Mathematics

Volume

159

Issue

6

Number of Pages

490-496

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.dam.2010.12.013

Socpus ID

79551545865 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/79551545865

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