Emergent Mind

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

(1702.08178)
Published Feb 27, 2017 in cs.DM and math.CO

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 $n$.

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