Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21516
Title: Improved upper bounds on the L(2,1) - labeling of the skew and converse skew product graphs
Authors: Shao, Z
Zhang, D 
Keywords: Channel assignment
Graph converse skew product
Graph skew product
L (2, 1)-labeling
Issue Date: 2008
Publisher: Elsevier
Source: Theoretical computer science, 2008, v. 400, no. 1-3, p. 230-233 How to cite?
Journal: Theoretical computer science 
Abstract: 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 | 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) 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 ∈ V (G)} = k. Griggs and Yeh conjecture that λ (G) ≤ Δ2 for any simple graph with maximum degree Δ ≥ 2. This paper considers the graph formed by the skew product and the converse skew product of two graphs with a new approach on the analysis of adjacency matrices of the graphs as in [W.C. Shiu, Z. Shao, K.K. Poon, D. Zhang, A new approach to the L (2, 1)-labeling of some products of graphs, IEEE Trans. Circuits Syst. II: Express Briefs (to appear)] and improves the previous upper bounds significantly.
URI: http://hdl.handle.net/10397/21516
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.02.048
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