The metric dimension of the circulant graph $C(n,\pm \{1,2,3,4\})$

Abstract

Let $G=(V,E)$ be a connected graph and let $d(u,v)$ denote the distance between vertices $u,v\in V$. A metric basis for $G$ is a set $B\subseteq V$ of minimum cardinality such that no two vertices of $G$ have the same distances to all points of $B$. The cardinality of a metric basis of $G$ is called the metric dimension of $G$, denoted by $\dim (G)$. In this paper we determine the metric dimension of the circulant graphs $C(n,\pm \{1,2,3,4\})$ for all values of $n$.