On a graph's security number

    Authors

    R. D. Dutton

    Comments

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    Abbreviated Journal Title

    Discret. Math.

    Keywords

    Alliances; Secure sets; Mathematics

    Abstract

    A secure set S subset of V of graph G = (V. E) is a set whose every nonempty subset can be successfully defended from an attack, under appropriate definitions of "attack" and "defended." The set S is secure when vertical bar N[X]boolean AND S vertical bar > = vertical bar N[X] - S vertical bar for every X subset of S. The smallest cardinality of a secure set in G is the security number of G. New bounds for the security number are established, the effect of some graph modifications on the security number is investigated, and the exact value of the security number for some families of graphs is given. (C) 2009 Elsevier B.V. All rights reserved.

    Journal Title

    Discrete Mathematics

    Volume

    309

    Issue/Number

    13

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    4443

    Last Page

    4447

    WOS Identifier

    WOS:000266760400028

    ISSN

    0012-365X

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