About Isolate Inclusive Sets in Graphs
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Keywords:
Isolate dominating set, minimal isolate dominating set, minimum isolate dominating set, isolate domination number, isolate inclusive set, private neighbourhoodAbstract
In this paper we further study isolate domination in graphs. In particular we study the effect of removing an edge 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 edge is removed from the graph. Further we also prove a necessary and sufficient condition under which the isoinc number increases when an edge is removed from the graph. We also consider the graphs for which isolate dominating number is equal to 1 or 2.
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