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

Li, Xiangwen, Mak-Hau, Vicky and Zhou, Sanming 2013, The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups, Journal of combinatorial optimization, vol. 25, no. 4, pp. 716-736.

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Title The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups
Author(s) Li, Xiangwen
Mak-Hau, VickyORCID iD for Mak-Hau, Vicky
Zhou, Sanming
Journal name Journal of combinatorial optimization
Volume number 25
Issue number 4
Start page 716
End page 736
Total pages 21
Publisher Springer
Place of publication New York, N. Y.
Publication date 2013-05
ISSN 1382-6905
Keyword(s) λ-Number
brick product
cayley graph
dihedral group
honeycomb toroidal graph
honeycomb torus
Summary 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.
Language eng
Field of Research 089999 Information and Computing Sciences not elsewhere classified
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2012, Springer Science+Business Media, LLC
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Created: Mon, 13 Aug 2012, 12:39:09 EST

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