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

TL;DR

This paper determines the metric dimension of circulant graphs with specific generators, providing exact values for all sizes, which advances understanding of graph metric properties.

Contribution

It explicitly calculates the metric dimension of $C(n,\u2206\{1,2,3,4 ight\})$ for all $n$, filling a gap in graph metric theory.

Findings

Exact metric dimension values for all $n$

Complete characterization of $C(n,\u2206\{1,2,3,4 ight\})$

Enhanced understanding of circulant graph metrics

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 $n$.