On the partition dimension of a class of circulant graphs

Title: On the partition dimension of a class of circulant graphs
Creator: Grigorious, Cyriac; Stephen, Sudeep; Rajan, Bharati; Miller, Mirka; William, Albert
Relation: Information Processing Letters Vol. 114, Issue 7, p. 353-356
Publisher Link: http://dx.doi.org/10.1016/j.ipl.2014.02.005
Publisher: Elsevier
Resource Type: journal article
Date: 2014
Description: For a vertex v of a connected graph G(V,E)G(V,E) and a subset S of V, the distance between a vertex v and S is defined by d(v,S)=min{d(v,x):x∈S}d(v,S)=min{d(v,x):x∈S}. For an ordered k -partition π={S1,S2…Sk}π={S1,S2…Sk} of V, the partition representation of v with respect to π is the k -vector r(v|π)=(d(v,S1),d(v,S2)…d(v,Sk))r(v|π)=(d(v,S1),d(v,S2)…d(v,Sk)). The k-partition π is a resolving partition if the k -vectors r(v|π)r(v|π), v∈V(G)v∈V(G) are distinct. The minimum k for which there is a resolving k-partition of V is the partition dimension of G. Salman et al. [1] in their paper which appeared in Acta Mathematica Sinica, English Series proved that partition dimension of a class of circulant graph G(n,±{1,2})G(n,±{1,2}), for all even n⩾6n⩾6 is four. In this paper we prove that it is three.
Subject: partition dimension; metric dimension; circulant graphs; interconnection networks
Identifier: http://hdl.handle.net/1959.13/1064444
Identifier: uon:17583
Identifier: ISSN:0020-0190
Language: eng
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