Labelling planar graphs without 4-cycles with a condition on distance two

  • Authors:

  • Weifan Wang;Leizhen Cai

  • Affiliations:

  • Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2008

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Abstract

Let p and q be positive integers. An L(p,q)-labelling of a graph G is a function @f:V(G)-N such that |@f(x)-@f(y)|=p if x and y are adjacent and |@f(x)-@f(y)|=q if x and y are of distance two apart. The L(p,q)-labelling number @l(G;p,q) of G is the least k for which G has an L(p,q)-labelling @f:V(G)-{0,1,...,k}. In this paper we prove that for every planar graph G without 4-cycles and of maximum degree @D,@l(G;p,q)=