A Lower bound for Secure Domination Number of an Outerplanar Graph

A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u ∈ S, there is a vertex v ∈ S such that $uv$ is an edge and (S \) ∪ \ is also a dominating set of G. The secure domination number of G, denoted by γₛ(G), is the cardinality of a smallest secure dominating sets of G. In this paper, we prove that for any outerplanar graph with n ≥ 4 vertices, γₛ(G) ≥ (n+4)/5 and the bound is tight.