A subset $S$ of vertices in a graph $G$ is a secure total dominating set of $G$ if $S$ is a total 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 total dominating set of $G$. We show that if $G$ is a maximal outerplanar graph of order $n$, then $G$ has a total secure dominating set of size at most $\lfloor 2n/3 \rfloor$. Moreover, if an outerplanar graph $G$ of order $n$, then each secure total dominating set has at least $\lceil (n+2)/3 \rceil$ vertices. We show that these bounds are best possible.

翻译：设图$G$的顶点子集$S$是$G$的一个安全全控制集，若$S$是$G$的全控制集，且对于每个顶点$u \not\in S$，存在顶点$v \in S$使得$uv$是一条边，且$(S \setminus \{v\}) \cup \{u\}$也是$G$的全控制集。我们证明：若$G$是阶数为$n$的极大外平面图，则$G$存在一个大小不超过$\lfloor 2n/3 \rfloor$的安全全控制集。此外，对于阶数为$n$的外平面图$G$，每个安全全控制集至少包含$\lceil (n+2)/3 \rceil$个顶点。我们证明这些界是最优的。