Split Domination Vertex Critical and Edge Critical Graphs - Girish V R; Usha P (Journal of the Indonesian Mathematical Society, 2020)
A dominating set D of a graph G = (V;E) is a split dominating set ifthe induced graph hV ???? 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(G????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.