A Characterization of 3-(γc, 2)-Critical Claw-Free Graphs Which are not 3-γc-Critical
dc.contributor.author | Ananchuen, Watcharaphong | |
dc.contributor.author | Ananchuen, Nawarat | |
dc.contributor.author | Caccetta, Louis | |
dc.date.accessioned | 2017-01-30T12:11:50Z | |
dc.date.available | 2017-01-30T12:11:50Z | |
dc.date.created | 2011-03-23T20:01:27Z | |
dc.date.issued | 2010 | |
dc.identifier.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. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/19085 | |
dc.identifier.doi | 10.1007/s00373-010-0920-2 | |
dc.description.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. | |
dc.publisher | Springer Japan KK | |
dc.subject | Critical graph | |
dc.subject | Connected domination | |
dc.subject | Claw-free | |
dc.title | A Characterization of 3-(γc, 2)-Critical Claw-Free Graphs Which are not 3-γc-Critical | |
dc.type | Journal Article | |
dcterms.source.volume | 26 | |
dcterms.source.startPage | 315 | |
dcterms.source.endPage | 328 | |
dcterms.source.issn | 0911-0119 | |
dcterms.source.title | Graphs and Combinatorics | |
curtin.department | Department of Mathematics and Statistics | |
curtin.accessStatus | Fulltext not available |