Some notes on the isolate domination in graphs
Nader Jafari Rad · AKCE International Journal of Graphs and Combinatorics · 2017
A subset S of vertices of a graph G is a dominating set of G if every vertex in V(G)−S has a neighbor in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. A dominating set S is an isolate dominating set if the induced subgraph G[S] has at least one isolated vertex. The isolate domination number γ0(G) is the minimum cardinality of an isolate dominating set of G. In this paper we study the complexity of the isolate domination in graphs, and obtain several bounds and characterizations on the isolate domination number, thus answering some open problems.