| A Note on L（2, 1）-labelling of Trees |
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| 引用本文： | Ming-qing ZHAI,Chang-hong LU,Jin-long SHU. A Note on L（2, 1）-labelling of Trees[J]. 应用数学学报(英文版), 2012, 28(2): 395-400. DOI: 10.1007/s10255-012-0151-9 |
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| 作者姓名： | Ming-qing ZHAI Chang-hong LU Jin-long SHU |
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| 作者单位： | [1]School of Mathematical Science, Nanjing Normal University, Jiangsu, Nanjing 210046, China [2]Department of Mathematics, Chuzhou University, Chuzhou 239012, China [3]Department of Mathematics, East China Normal University, Shanghai 200241, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (No. 10971248,11101057);Anhui Provincial Natural Science Foundation (No. 10040606Q45);Postdoctoral Science Foundation of Jiangsu Provinc (No.1102095C) |
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| 摘 要： | 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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| 关 键 词： | 标签 非负整数集 顶点集 树木 函数 数学 |
A note on L(2, 1)-labelling of trees |
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| Ming-qing Zhai,Chang-hong Lu,Jin-long Shu. A note on L(2, 1)-labelling of trees[J]. Acta Mathematicae Applicatae Sinica, 2012, 28(2): 395-400. DOI: 10.1007/s10255-012-0151-9 |
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| Authors: | Ming-qing Zhai Chang-hong Lu Jin-long Shu |
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| Affiliation: | 1 School of Mathematical Science,Nanjing Normal University,Jiangsu,Nanjing 210046,China 2 Department of Mathematics,Chuzhou University,Chuzhou 239012,China 3 Department of Mathematics,East China Normal University,Shanghai 200241,China |
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| 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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| Keywords: | distance-two labelling L(2,1)-labelling tree |
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