Affordable Access

Access to the full text

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

Authors
  • Li, Xiangwen1
  • Mak-Hau, Vicky2
  • Zhou, Sanming3
  • 1 Central China Normal University, Department of Mathematics, Wuhan, 430079, China , Wuhan (China)
  • 2 Deakin University, School of Information Technology, Burwood, VIC, 3125, Australia , Burwood (Australia)
  • 3 The University of Melbourne, Department of Mathematics and Statistics, Parkville, VIC, 3010, Australia , Parkville (Australia)
Type
Published Article
Journal
Journal of Combinatorial Optimization
Publisher
Springer-Verlag
Publication Date
Jul 10, 2012
Volume
25
Issue
4
Pages
716–736
Identifiers
DOI: 10.1007/s10878-012-9525-4
Source
Springer Nature
Keywords
License
Yellow

Abstract

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.

Report this publication

Statistics

Seen <100 times