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    A Characterization of 3-(γc, 2)-Critical Claw-Free Graphs Which are not 3-γc-Critical

    Access Status
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    Authors
    Ananchuen, Watcharaphong
    Ananchuen, Nawarat
    Caccetta, Louis
    Date
    2010
    Type
    Journal Article
    
    Metadata
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    Citation
    Ananchuen, Watcharaphong and Ananchuen, Nawarat and Caccetta, Louis. 2010. A Characterization of 3-(γc, 2)-Critical Claw-Free Graphs Which are not 3-γc-Critical. Graphs and Combinatorics. 26 (3): pp. 315-328.
    Source Title
    Graphs and Combinatorics
    DOI
    10.1007/s00373-010-0920-2
    ISSN
    0911-0119
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/19085
    Collection
    • Curtin Research Publications
    Abstract

    Let γ c (G) denote the minimum cardinality of a connected dominating set for G. A graph G is k-γ c -critical if γ c (G) = k, but γ c (G + xy) < k for xy Î E([`(G)])xyE(G) . Further, for integer r ≥ 2, G is said to be k-(γ c , r)-critical if γ c (G) = k, but γ c (G + xy) < k for each pair of non-adjacent vertices x and y that are at distance at most r apart. k-γ c -critical graphs are k-(γ c , r)-critical but the converse need not be true. In this paper, we give a characterization of 3-(γ c , 2)-critical claw-free graphs which are not 3-γ c -critical. In fact, we show that there are exactly four classes of such graphs.

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