Abstract:
The doubly dominating set of a graph G is a set of dominating set S\ss V(G) such that both \ll S\rr and \ll V(G)\ssm S\rr have an isolated vertex. The cardinality of a doubly isolate dominating set with minimum cardinality is called doubly isolate domination number and is denoted by \00(G). In this paper, we characterize the doubly isolate dominating set for the corona and lexicographic product of two graphs.