Global secure sets of grid-like graphs

    Authors

    Y. Y. Ho;R. Dutton

    Comments

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    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

    WOS:000289707900009

    ISSN

    0166-218X

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