• ABOUT ISOLATE DOMINATION IN GRAPHS

D. K. THAKKAR, N. J. SAVALIYA*

Abstract


In this paper we further study isolate domination in graphs. In particular we study the effect of removing an isolated vertex from the graph on the isolate domination number of the graph. We prove a necessary and sufficient condition under which the isolate domination number increases when an isolated vertex is remove from the graph. Further we also prove a necessary and sufficient condition under which the isolate domination number decreases when an isolated vertex is remove from the graph.  It follows that if a graph  has an isolated vertex then  is the only isolated vertex of the graph .For a non isolated vertex of a graph, we prove similar results.


Keywords


isolate dominating set, minimal isolate dominating set, minimum isolate dominating set, isolate domination number, isolate inclusive set, 1-maximal isolate inclusive set, privateneighborhood.

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