English

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

Discrete Mathematics 2018-01-17 v2 Combinatorics

Abstract

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

Keywords

Cite

@article{arxiv.1702.08178,
  title  = {The metric dimension of the circulant graph $C(n,\pm\{1,2,3,4\})$},
  author = {Cyriac Grigorious and Thomas Kalinowski and Joe Ryan and Sudeep Stephen},
  journal= {arXiv preprint arXiv:1702.08178},
  year   = {2018}
}