New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs

  • Authors:

  • Ziming Duan;Pingli Lv;Lianying Miao;Zhengke Miao;Cuiqi Wang

  • Affiliations:

  • College of Science, China University of Mining and Technology, Xuzhou 221116, PR China;School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, PR China and Xuhai College, China University of Mining and Technology, Xuzhou 221008, PR China;College of Science, China University of Mining and Technology, Xuzhou 221116, PR China;School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, PR China;College of Science, China University of Mining and Technology, Xuzhou 221116, PR China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

An L(2,1)-labeling of a graph G is defined as a function f from the vertex set V(G) into the nonnegative integers such that for any two vertices x, y, |f(x)-f(y)|=2 if d(x,y)=1 and |f(x)-f(y)|=1 if d(x,y)=2, where d(x,y) is the distance between x and y in G. The L(2,1)-labeling number @l"2","1(G) of G is the smallest number k such that G has an L(2,1)-labeling with k=max{f(x)|x@?V(G)}. In this paper, we consider the graph formed by the skew product and converse skew product of two graphs, and give new upper bounds of the L(2,1)-labeling number, which improves the upper bounds obtained by Shao and Zhang [Z.D. Shao, D. Zhang, Improved upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs, Theoret. Comput. Sci. 400 (2008) 230-233] in many cases.