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：图$G$中顶点子集$S$称为$G$的安全全控制集，当且仅当$S$是$G$的全控制集，且对于每个不属于$S$的顶点$u$，存在$v \in S$使得$uv$为边且$(S \setminus \{v\}) \cup \{u\}$仍是$G$的全控制集。本文证明：若$G$为$n$阶极大外平面图，则$G$存在至多$\lfloor 2n/3 \rfloor$个顶点的全安全控制集。此外，对于$n$阶外平面图$G$，每个安全全控制集至少包含$\lceil (n+2)/3 \rceil$个顶点。本文证明这些界限是最优的。