Split Domination Vertex Critical and Edge Critical Graphs
Abstract
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(Gv) < 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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