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

Xiangwen Li (), Vicky Mak-Hau () and Sanming Zhou ()
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Xiangwen Li: Central China Normal University
Vicky Mak-Hau: Deakin University
Sanming Zhou: The University of Melbourne

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 18, 716-736

Abstract: 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.

Keywords: L(2; 1)-labelling; λ-Number; Brick product; Honeycomb toroidal graph; Honeycomb torus; Cayley graph; Dihedral group (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-012-9525-4

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