Some notes on the isolate domination in graphs

Abstract

A subset of vertices of a graph is a dominating set of if every vertex in has a neighbor in . The domination number is the minimum cardinality of a dominating set of . A dominating set is an isolate dominating set if the induced subgraph has at least one isolated vertex. The isolate domination number is the minimum cardinality of an isolate dominating set of . 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.

Keywords

• domination
• isolate domination
• total domination
• complexity