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The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups

journal contribution
posted on 2013-05-01, 00:00 authored by X Li, Vicky MakVicky Mak, S Zhou
A k-L(2,1)-labelling of a graph G is a mapping f:V(G)→{0,1,2,…,k} such that |f(u)−f(v)|≥2 if uv∈E(G) and f(u)≠f(v) if u,v are distance two apart. The smallest positive integer k such that G admits a k-L(2,1)-labelling is called the λ-number of G. In this paper we study this quantity for cubic Cayley graphs (other than the prism graphs) on dihedral groups, which are called brick product graphs or honeycomb toroidal graphs. We prove that the λ-number of such a graph is between 5 and 7, and moreover we give a characterisation of such graphs with λ-number 5.

History

Journal

Journal of combinatorial optimization

Volume

25

Issue

4

Pagination

716 - 736

Publisher

Springer

Location

New York, N. Y.

ISSN

1382-6905

eISSN

1573-2886

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2012, Springer Science+Business Media, LLC