Some Results on Point Set Domination of Fuzzy Graphs

Let G be a fuzzy graph. Let γ(G), γ_p(G) denote respectively the domination number, the point set domination number of a fuzzy graph. A dominating set D of a fuzzy graph is said to be a point set dominating set of a fuzzy graph if for every S⊆V-D there exists a node d∈D such that 〈S ∪ {d}〉 is a connected fuzzy graph. The minimum cardinality taken over all minimal point set dominating set is called a point set domination number of a fuzzy graph G and it is denoted by γ_p(G). In this paper we concentrate on the point set domination number of a fuzzy graph and obtain some bounds using the neighbourhood degree of fuzzy graphs.