Strong Weak Secure Domination in Graphs

Abstract

Let G be a graph. A subset X of V is a Secure Dominating Set(SDS)[5] if for every in , there exists some in adjacent to such that is a dominating set. A SDS of V is called a Strong Secure Dominating Set(SSDS) if for every in , there exists some in such that Similarly, Weak Secure Dominating Set(WSDS) is defined. The minimum cardinality of a strong(weak) secure dominating set is denoted by ()( . We initiate a study on these parameters and some bounds related to them are obtained.