Note: The L(2,1)-labelling of trees

  • Authors:
  • Wei-Fan Wang

  • Affiliations:
  • Department of Mathematics, Zhejiang Normal University, Jinhua 321004, PR China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2006

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Abstract

An L(2,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices have numbers at least 2 apart, and vertices at distance 2 have distinct numbers. The L(2,1)-labelling number @l(G) of G is the minimum range of labels over all such labellings. It was shown by Griggs and Yeh [Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586-595] that every tree T has @D+1=