Strong Co-Secure Domination in Graphs.

Let G = (V, E) be a graph. A subset D of the vertex set V(G) of a graph G is a strong co-secure dominating set if every vertex v ∈ V - D there exists u ∈ D such that uv ∈ E(G) then D\{u} ∪ {v} and deg(u) ≥ deg(v). The strong co-secure domination number is the minimum cardinality of a strong co-secure dominating set of G, and it is denoted by yscsd (G). The strong co-secure dominating set of G is found for path, cycle, helm graph, closed helm graph, Petersen graph, gear graph, Tadpole graph, and Butterfly graph. [ABSTRACT FROM AUTHOR]