Metric Dimension of Generalized Theta Graphs

Abstract

A vertex $w$ in a graph $G$ is said to resolve two vertices $u$ and $v$ if $d(w,u)\ne d(w,v)$. A set $W$ of vertices is a resolving set for $G$ if every pair of distinct vertices is resolved by some vertex in $W$. The metric dimension of $G$ is the minimum cardinality of such a set. In this paper, we investigate the metric dimension of generalized theta graphs, providing exact values and structural insights for several subclasses.

16 pages, multiple figures