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dc.contributor.authorKaemawichanurat, P.
dc.contributor.authorCaccetta, Louis
dc.contributor.authorAnanchuen, N.
dc.date.accessioned2017-01-30T11:52:35Z
dc.date.available2017-01-30T11:52:35Z
dc.date.created2016-04-26T19:30:22Z
dc.date.issued2016
dc.identifier.citationKaemawichanurat, P. and Caccetta, L. and Ananchuen, N. 2016. Critical graphs with respect to total domination and connected domination. Australasian Journal of Combinatorics. 65 (1): pp. 1-13.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/15897
dc.description.abstract

A graph G is said to be k-γt -critical if the total domination number γt(G)= k and γt (G + uv) < k for every uv /∈ E(G). A k-γc-critical graph G is a graph with the connected domination number γc(G) = k and γc(G + uv) < k for every uv /∈ E(G). Further, a k-tvc graph is a graph with γt(G) = k and γt (G − v) < k for all v ∈ V(G), where v is not a support vertex (i.e. all neighbors of v have degree greater than one). A 2-connected graph G is said to be k-cvc if γc(G) = k and γc (G − v) < k for all v ∈ V(G). In this paper, we prove that connected k-γt -critical graphs and k-γc-critical graphs are the same if and only if 3 ≤ k ≤ 4. For k ≥ 5, we concentrate on the class of connected k-γt-critical graphs G with γc (G) = k and the class of k-γc-critical graphs G with γt(G) = k. We show that these classes intersect but they do not need to be the same. Further, we prove that 2-connected k-tvc graphs and k-cvc graphs are the same if and only if 3 ≤ k ≤ 4. Similarly, for k ≥ 5, we focus on the class of 2-connected k-tvc graphs G with γc (G) = k and the class of 2-connected k-cvc graphs G with γt (G) = k. We finish this paper by showing that these classes do not need to be the same.

dc.publisherCentre for Discrete Mathematics and Computing
dc.titleCritical graphs with respect to total domination and connected domination
dc.typeJournal Article
dcterms.source.volume65
dcterms.source.number1
dcterms.source.startPage1
dcterms.source.endPage13
dcterms.source.titleAustralasian Journal of Combinatorics
curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusFulltext not available


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