PT  - JOURNAL ARTICLE
AU  - Ahmad, Ali
AU  - Sultan, Saba
TI  - On Minimal Doubly Resolving Sets of Circulant Graphs
DP  - 2017 Mar 31
TA  - Acta Mechanica Slovaca
PG  - 6--11
VI  - 21
IP  - 1
AID - 10.21496/ams.2017.002
IS  - 13352393
AB  - Consider a simple connected undirected graph G = (VG ,EG), where VG represents the vertex set and EG represents the edge set respectively. A subset B of VG is called a resolving set if for every two distinct vertices x, y of G there is a vertex v in set B such that d(x,v) ≠ d(y,v). The resolving set of minimum cardinality is called metric basis of graph G . This minimal cardinality of metric basis is denoted by β(G), and is called metric dimension of G. A subset D of V is called doubly resolving set if for every two vertices x, y of G there are two vertices u, v ∈ D such that d(u,x) -d(u,y) ≠ d(v,x) -d(v,y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G).Some partial cases for metric dimension of circulant graph Cn(1,2,3) for n ≥ 12 has been discussed in [21]. Afterwards, problem of finding metric dimension for circulant graph Cn(1,2,3), n ≥ 12 has been completely solved by Borchert et al., in [7].In this paper, we prove that ψ (Cn (1, 2, 3)) = β (Cn (1, 2, 3)) = {4 if n ≠ 1(mod 6), 5 otherwise.