2SSD (G). The 2-step secure dominating set of G is found for path, cycle, ladder graph, Peterson graph, wheel graph, Helm graph, closed helm graph.
">This paper introduces a new parameter called 2-step secure domination of a graph with real world applications. Let G = (V, E) be a graph. A subset D of a vertices in a graph G is 2-step secure dominating set if every vertex v ϵ V - D, there exist one vertex uϵD such that d(u, v) = 2, and if each vertex uϵV-D is adjacent to a vertex vϵD such that (D-{v})υ{u} is a dominating set. The minimum cardinality of such a set is called the 2-step secure domination G, denoted by γ2SSD (G). The 2-step secure dominating set of G is found for path, cycle, ladder graph, Peterson graph, wheel graph, Helm graph, closed helm graph.