Circular L(j,k)-labeling number of direct product of path and cycle

  • Authors:

  • Qiong Wu;Wai Chee Shiu;Pak Kiu Sun

  • Affiliations:

  • Department of Mathematics, Hong Kong Baptist University, Hong Kong, China;Department of Mathematics, Hong Kong Baptist University, Hong Kong, China;Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

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Abstract

Let j, k and m be positive numbers, a circular m-L(j,k)-labeling of a graph G is a function f:V(G)驴[0,m) such that |f(u)驴f(v)| m 驴j if u and v are adjacent, and |f(u)驴f(v)| m 驴k if u and v are at distance two, where |a驴b| m =min{|a驴b|,m驴|a驴b|}. The minimum m such that there exist a circular m-L(j,k)-labeling of G is called the circular L(j,k)-labeling number of G and is denoted by 驴 j,k (G). In this paper, for any two positive numbers j and k with j≤k, we give some results about the circular L(j,k)-labeling number of direct product of path and cycle.