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

Qiong Wu (), Wai Chee Shiu () and Pak Kiu Sun ()
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Qiong Wu: Hong Kong Baptist University
Wai Chee Shiu: Hong Kong Baptist University
Pak Kiu Sun: Hong Kong Baptist University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 2, No 11, 355-368

Abstract: 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)→[0,m) such that |f(u)−f(v)| m ≥j if u and v are adjacent, and |f(u)−f(v)| m ≥k if u and v are at distance two, where |a−b| m =min{|a−b|,m−|a−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 σ 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.

Keywords: Circular L(j; k)-labeling; Direct product (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9520-9

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