dc.contributor.author Kaemawichanurat, P. dc.contributor.author Caccetta, Louis dc.contributor.author Ananchuen, N. dc.date.accessioned 2019-02-19T04:16:15Z dc.date.available 2019-02-19T04:16:15Z dc.date.created 2019-02-19T03:58:21Z dc.date.issued 2018 dc.identifier.citation Kaemawichanurat, P. and Caccetta, L. and Ananchuen, N. 2018. Bounds on the order of connected domination vertex critical graphs. Journal of Combinatorial Mathematics and Combinatorial Computing. 107: pp. 73-96. dc.identifier.uri http://hdl.handle.net/20.500.11937/74215 dc.description.abstract A vertex subset D of G is a dominating set of G if every vertex in V(G)-D is adjacent to a vertex in D. Moreover, a dominating set D of G is a connected dominating set if G[D] is connected. The minimum cardinality of a connected dominating set of G is called the connected domination number of G and is denoted by yc(G). A graph G is said to be fc-yc-vertex critical if yc(G) = k and yc(G-v) < k for any vertex v of G. In this paper, we establish the order of k-yc-vertex critical graphs in terms of k and the maximum degree A. We prove that a Jt-yc.-vertexcritical graph has A + k 3 when A is even. It has been proved that every k-yc-vertex critical graph achieving the upper bound is A-regular for k = 2 or 3. For k = 4, we prove that every 4-yc-vertex critical graph achieving the upper bound is A-regular. We further show that, for k = 2,3 or 4, there exists a Jt-yc-vertex critical graph of order (A-l)(fc-l) + 3 if and only if A is even. We characterize, for k > 5, that every k-yc-vertex critical graph of order A + k is isomorphic to the cycle of length k + 2. dc.publisher Elsevier dc.title Bounds on the order of connected domination vertex critical graphs dc.type Journal Article dcterms.source.volume 107 dcterms.source.startPage 73 dcterms.source.endPage 96 dcterms.source.issn 0835-3026 dcterms.source.title Journal of Combinatorial Mathematics and Combinatorial Computing curtin.department School of Electrical Engineering, Computing and Mathematical Science (EECMS) curtin.accessStatus Fulltext not available
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