Equitable isolate domination in graphs

Abstract

A subset S ⊆ V(G) is said to an equitable isolate dominating set of a graph G if it is both equitable dominating set of G and isolate dominating set of G. The minimum cardinality of an equitable isolate dominating set is called equitable isolate domination number of G and is denoted by γ_e0 (G). An equitable isolate dominating set S of G is called γ_e0 -set of G. In this paper, the authors give characterizations of equitable isolate dominating set of some graphs and graphs obtained from the join and corona of two graphs. Furthermore, the equitable isolate domination numbers of these graphs is determined, and the graphs with no equitable isolate dominating sets are investigated.