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

Author

Listed:
  • Xiangwen Li

    (Central China Normal University)

  • Vicky Mak-Hau

    (Deakin University)

  • Sanming Zhou

    (The University of Melbourne)

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.

Suggested Citation

  • Xiangwen Li & Vicky Mak-Hau & Sanming Zhou, 2013. "The L(2,1)-labelling problem for cubic Cayley graphs on dihedral groups," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 716-736, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-012-9525-4
    DOI: 10.1007/s10878-012-9525-4
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    Cited by:

    1. Huijuan Wang & Lidong Wu & Xin Zhang & Weili Wu & Bin Liu, 2016. "A note on the minimum number of choosability of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1013-1022, April.
    2. Huijuan Wang & Bin Liu & Xin Zhang & Lidong Wu & Weili Wu & Hongwei Gao, 2016. "List edge and list total coloring of planar graphs with maximum degree 8," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 188-197, July.
    3. Zehui Shao & Jin Xu & Roger K. Yeh, 2016. "$$L(2,1)$$ L ( 2 , 1 ) -labeling for brick product graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 447-462, February.
    4. Huijuan Wang & Lidong Wu & Weili Wu & Jianliang Wu, 2014. "Minimum number of disjoint linear forests covering a planar graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 274-287, July.

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