(untitled) (European Journal of Pure and Applied Mathematics, 2024)
A subset S V(G) is said to be a perfect equitable isolate dominating set of a graph G if it is both perfect equitable dominating set of G and isolate dominating set of G. The minimum cardinality of a perfect equitable isolate dominating set is called perfect equitable isolate domination number of G and is denoted by γ_pe0(G). A perfect equitable isolate dominating set S of G is called γ_pe0-set of G. In this paper, the authors give characterizations of a perfect equitable isolate dominating set of some graphs and graphs obtained from the join and corona of two graphs. Furthermore, the perfect equitable isolate domination numbers of these graphs is determined, and the graphs with no perfect equitable isolate dominating sets are investigated.