Secure Support Strong Domination in Graphs - Guruviswanathan, R.; Ayyampillai, M.; Swaminathan, V. (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, \(v \in D\) such that \(uv \in E(G)\) and \(supp(u) ≥ supp(v)\) and \((D-\{v\})\cup \{u\}\) 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.