Perfect Isolate Domination in Graphs (European Journal of Pure and Applied Mathematics, 2023)
Let G = (V (G), E(G)) be a simple connected graph. A set S ⊆ V (G) is said to be a perfect isolate dominating set of G if S is a perfect dominating set and an isolate dominating set of G. The minimum cardinality of a perfect isolate dominating set of G is called perfect isolate domination number, and is denoted by γp0(G). A perfect isolate dominating set S with |S| = γp0(G) is said to be γp0-set. In this paper, the author gives a characterization of perfect isolate dominating set of some graphs and graphs obtained from the join, corona and lexicographic product of two graphs. Moreover, the perfect isolate domination number of the forenamed graphs is determined and also, graphs having no perfect isolate dominating set are examined.
Keywords: perfect domination number, perfect dominating set, isolate domination number, isolate dominating set, perfect isolate domination number and perfect isolate dominating set