Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/17986
Title: Distance labellings of graphs
Authors: Shao, Z 
Zhang, D 
Issue Date: 2013
Source: Ars combinatoria, 2013, v. 108, p. 23-31 How to cite?
Journal: Ars Combinatoria 
Abstract: An L(2, 1)-labelling 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)-labelling number λ(G) of G is the smallest number k such that G has an L(2, 1)-labelling with max{f(v) : v € V(G)} = k. Griggs and Yeh conjecture that λ(G) ≤ Δ2 for any simple graph with maximum degree A Δ≥ 2. This article considers the graphs formed by the cartesian product of n(n ≥ 2) graphs. The new graph satisfies the above conjecture (with minor exceptions). Moreover, we generalize our results in [19].
URI: http://hdl.handle.net/10397/17986
ISSN: 0381-7032
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