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)

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.