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 \v\) \u\ is also a dominating set of G. The secure domination number of G, denoted by ₒ (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, ₒ (G) (n+4) /5 and the bound is tight.