Title
Global secure sets of grid-like graphs
Abbreviated Journal Title
Discret Appl. Math.
Keywords
Security number; Dominating set; Cycle; Cartesian product; Grid graph; NUMBER; Mathematics, Applied
Abstract
Let G = (V. E) be a graph and S subset of V. The set S is a secure set if for all X subset of S, vertical bar N vertical bar X vertical bar boolean AND S vertical bar > = vertical bar N vertical bar X vertical bar-S vertical bar, 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 gamma(s)(G). The sets studied in this paper are different from secure dominating sets studied in Cockayne et al. (2003) 131, Grobler and Mynhardt (2009) [81, or Klostermeyer and Mynhardt (2008) [13], which are also denoted by gamma(s). In this paper, we provide results on the global security numbers of paths, cycles and their Cartesian products. Published by Elsevier B.V.
Journal Title
Discrete Applied Mathematics
Volume
159
Issue/Number
6
Publication Date
1-1-2011
Document Type
Article
Language
English
First Page
490
Last Page
496
WOS Identifier
ISSN
0166-218X
Recommended Citation
"Global secure sets of grid-like graphs" (2011). Faculty Bibliography 2010s. 1387.
https://stars.library.ucf.edu/facultybib2010/1387
Comments
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