A new approach to the L(2, 1)-labeling of some products of graphs

Wai Chee Shiu*, Zhendong Shao, Kin Keung Poon, David Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)


The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that vert f(x) - f(y)\vert ≥ 2 if d(x,y) = 1 and vert f(x) - f(y)≥ 1 if d(x,y) = 2, where d(x,y) denotes the distance between x and y in G. The L(2, 1)-labeling number λ (G)of G is the smallest number k such that G has an L(2, 1)-labeling with max f(v):v\in V(G) = k. In this paper, we develop a dramatically new approach on the analysis of the adjacency matrices of the graphs to estimate the upper bounds of λ-numbers of the four standard graph products. By the new approach, we can achieve more accurate results and with significant improvement of the previous bounds.

Original languageEnglish
Pages (from-to)802-805
Number of pages4
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number8
Publication statusPublished - Aug 2008

Scopus Subject Areas

  • Electrical and Electronic Engineering

User-Defined Keywords

  • Cartesian product
  • Channel assignment
  • Direct product
  • L(2,1)-labeling
  • Lexicographic product
  • Strong product


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