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arxiv: 1702.08178 · v2 · pith:LQFGT7U5new · submitted 2017-02-27 · 💻 cs.DM · math.CO

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

classification 💻 cs.DM math.CO
keywords metricdimensionbasiscardinalitycirculantgraphverticescalled
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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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