The metric dimension of the circulant graph C(n,±{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∈𝑉. A metric basis for 𝐺 is a set 𝐵⊆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,±{1,2,3,4}) for all values of 𝑛.