Isolate Domination in Unicyclic Graphs
I. Sahul Hamid, S. Balamurugan · International Journal of Mathematics and Soft Computing · 2013
A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. A dominating set D such that has an isolated vertex is called an isolate dominating set and the minimum cardinality of an isolate dominating set is called the isolate domination number of G and is denoted by γ0(G). In this paper we characterize the unicyclic graphs in which the order equals the sum of the isolate domination number and its maximum degree.