On the general position numbers of maximal outerplanar graphs

TL;DR

This paper investigates the maximum size of general position sets in maximal outerplanar graphs, establishing bounds and characterizing extremal graphs, thereby advancing understanding of graph geometric properties.

Contribution

It provides the first bounds on general position numbers for maximal outerplanar graphs and characterizes the extremal cases.

Findings

Established bounds on gp-numbers for maximal outerplanar graphs.

Characterized extremal graphs achieving these bounds.

Enhanced understanding of geometric properties in specific graph classes.

Abstract

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 $gp(G)=\max\{|R|:R\in\mathcal{R}\}$. In this paper, we determine the bounds on the gp-numbers for any maximal outerplane graph and characterize the corresponding extremal graphs.