A note on isolate domination - Ismail Sahul Hamid; S. Balamurugan; A. Navaneethakrishnan (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2016)
A set S of vertices of a graph G such that S has an isolated vertex is called an isolate set of G. The minimum and maximum cardinality of a maximal isolate set are called the isolate number i_0(G) and the upper isolate number I_0(G) respectively. An isolate set that is also a dominating set (an irredundant set) is an isolate dominating set (an isolate irredundant set). The isolate domination number γ_0(G) and the upper isolate domination number Γ_0(G) are respectively the minimum and maximum cardinality of a minimal isolate dominating set while the isolate irredundance number ir_0(G) and the upper isolate irredundance number IR_0(G) are the minimum and maximum cardinality of a maximal isolate irredundant set of G. The notion of isolate domination was introduced in sb and the remaining were introduced in isrn. This paper further extends a study of these parameters.