(untitled) (Journal of Informatics and Mathematical Sciences, 2017)
Let \(G=(V, E)\) be a simple finite undirected graph. Let \(D\) be a subset of \(V(G)\). \(D\) is called a secure support strong dominating set of \(G\) (also called very excellent support strong dominating set), if \(D\) is a support strong dominating set of \(G\) and for any \(u\) in \(V-D\), there exists a, \(v D\) such that \(uv E(G)\) and \(supp(u) ≥ supp(v)\) and \((D-{v}){u}\) is support dominating set. The minimum cardinality of a secure support strong dominating set of \(G\) is called the secure support strong domination number of \(G\) and is denoted by \(γ_sec^ss(G)\). In this paper, properties of the new parameters are derived and its relationships with other parameters are studied.