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V R, Girish
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Mathematics

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Split Domination Vertex Critical and Edge Critical Graphs V R, Girish; P, Usha
Journal of the Indonesian Mathematical Society Volume 26 Number 1 (March 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.1.772.55-63

Abstract

A dominating set D of a graph G = (V;E) is a split dominating set ifthe induced graph hV ô€€€ Di is disconnected. The split domination number s(G)is the minimum cardinality of a split domination set. A graph G is called vertexsplit domination critical if s(Gô€€€v) s(G) for every vertex v 2 G. A graph G iscalled edge split domination critical if s(G + e) s(G) for every edge e in G. Inthis paper, whether for some standard graphs are split domination vertex critical ornot are investigated and then characterized 2- ns-critical and 3- ns-critical graphswith respect to the diameter of a graph G with vertex removal. Further, it is shownthat there is no existence of s-critical graph for edge addition.
Co-Authors P, Usha