Abstract
An L(2, 1)-labelling of a graph G is a function from the vertex set V (G) to the set of all nonnegative integers such that |f(u) − f(v)| ≥ 2 if d G (u, v) = 1 and |f(u) − f(v)| ≥ 1 if d G (u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by λ(G), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598–603].
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Supported by the National Natural Science Foundation of China (No. 10971248, 11101057), Anhui Provincial Natural Science Foundation (No. 10040606Q45) and Postdoctoral Science Foundation of Jiangsu Provinc (No. 1102095C).
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Zhai, Mq., Lu, Ch. & Shu, Jl. A note on L(2, 1)-labelling of trees. Acta Math. Appl. Sin. Engl. Ser. 28, 395–400 (2012). https://doi.org/10.1007/s10255-012-0151-9
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DOI: https://doi.org/10.1007/s10255-012-0151-9