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 $u \not\in S$, there is a vertex $v \in S$ such that $uv$ is an edge and $(S \setminus \{v\}) \cup \{u\}$ is also a dominating set of $G$. The secure domination number of $G$, denoted by $\gamma_{s}(G)$, is the cardinality of a smallest secure dominating sets of $G$. In this paper, we prove that for any outerplanar graph with $n \geq 4$ vertices, $\gamma_{s}(G) \geq (n+4)/5$ and the bound is tight.

翻译：图$G$的一个顶点子集$S$被称为$G$的安全控制集，当且仅当$S$是$G$的一个控制集，且对于每个顶点$u \not\in S$，存在一个顶点$v \in S$使得$uv$是边，并且$(S \setminus \{v\}) \cup \{u\}$也是$G$的一个控制集。$G$的安全控制数，记为$\gamma_{s}(G)$，是$G$的最小安全控制集的基数。本文证明，对于任意具有$n \geq 4$个顶点的外平面图，有$\gamma_{s}(G) \geq (n+4)/5$，且该界是紧的。