On the general position numbers of maximal outerplanar graphs

A subset $R\subseteq V(G)$ of a graph $G$ is a general position set if any triple set $R_0$ of $R$ is non-geodesic in $G$, that is, no vertex of $R_0$ lies on any geodesic between the other two vertices of $R_0$ in $G$. Let $\mathcal{R}$ be the set of general position sets of a graph $G$. The general position number of a graph $G$, denoted by $gp(G)$, is defined as $gp(G)=\max \{\mathrm{\mid }R\mathrm{\mid }:R\in \mathcal{R}\}$. In this paper, we determine the bounds on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs.