On global domination critical graphs

    Authors

    R. D. Dutton;R. C. Brigham

    Comments

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    Abbreviated Journal Title

    Discret. Math.

    Keywords

    Domination; Global domination; Changing and unchanging; Mathematics

    Abstract

    A dominating set of a graph G = (V, E) is a subset S subset of V such that every vertex not in S is adjacent to at least one vertex of S. The domination number of G is the cardinality of a smallest dominating set. The global domination number, gamma(g)(G), is the cardinality, of a smallest set S that is simultaneously a dominating set of both G and its complement (G) over bar. Graphs for which gamma(g)(G - e) > gamma(g)(G) for all edges e is an element of E are characterized, as are graphs for which gamma(e)(G - e) < gamma(e)(G) for all edges e is an element of E whenever < (G)over bar > is disconnected. Progress is reported in the latter case when (G) over bar is connected. Published by Elsevier B.V.

    Journal Title

    Discrete Mathematics

    Volume

    309

    Issue/Number

    19

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    5894

    Last Page

    5897

    WOS Identifier

    WOS:000271375700013

    ISSN

    0012-365X

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