A Characterization of 3(γc, 2)Critical ClawFree Graphs Which are not 3γcCritical
Abstract
Let γ c (G) denote the minimum cardinality of a connected dominating set for G. A graph G is kγ 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 nonadjacent vertices x and y that are at distance at most r apart. kγ 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 clawfree graphs which are not 3γ c critical. In fact, we show that there are exactly four classes of such graphs.
Citation
Ananchuen, Watcharaphong and Ananchuen, Nawarat and Caccetta, Louis. 2010. A Characterization of 3(γc, 2)Critical ClawFree Graphs Which are not 3γcCritical. Graphs and Combinatorics. 26 (3): pp. 315328.
Source Title
Graphs and Combinatorics
ISSN
School
Department of Mathematics and Statistics
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