Extremal problems on consecutive L(2,1)-labelling

  • Authors:

  • Changhong Lu;Lei Chen;Mingqing Zhai

  • Affiliations:

  • Department of Mathematics, East China Normal University, Shanghai 200062, PR China and Institute of Theoretical Computing, East China Normal University, Shanghai 200062, PR China;Department of Mathematics, East China Normal University, Shanghai 200062, PR China;Department of Mathematics and Computer Science, Chuzhou University, Chuzhou, Anhui 239012, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

For a given graph G of order n, a k-L(2,1)-labelling is defined as a function f:V(G)-{0,1,2,...,k} such that |f(u)-f(v)|=2 when d"G(u,v)=1 and |f(u)-f(v)|=1 when d"G(u,v)=2. The L(2,1)-labelling number of G, denoted by @l(G), is the smallest number k such that G has a k-L(2,1)-labelling. The consecutive L(2,1)-labelling is a variation of L(2,1)-labelling under the condition that the labelling f is an onto function. The consecutive L(2,1)-labelling number of G is denoted by @l@?(G). Obviously, @l(G)=