Girish V R, Usha P


A dominating set D of a graph G = (V;E) is a split dominating set if
the 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 vertex
split domination critical if s(G􀀀v) < s(G) for every vertex v 2 G. A graph G is
called edge split domination critical if s(G + e) < s(G) for every edge e in G. In
this paper, whether for some standard graphs are split domination vertex critical or
not are investigated and then characterized 2- ns-critical and 3- ns-critical graphs
with respect to the diameter of a graph G with vertex removal. Further, it is shown
that there is no existence of s-critical graph for edge addition.

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DOI: https://doi.org/10.22342/jims.26.1.772.55-63


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