| 最大度为3的树的L(2,1)-标号数的一个刻画 |
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| 引用本文： | 陈东,邵慰慈,舒巧君,辛百桥,王维凡.最大度为3的树的L(2,1)-标号数的一个刻画[J].数学学报,2016,59(5):685-710. |
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| 作者姓名： | 陈东 邵慰慈 舒巧君 辛百桥 王维凡 |
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| 作者单位： | 1. 浙江师范大学行知学院 金华 321004;
2. 香港浸会大学数学系 香港;
3. 杭州电子科技大学理学院 杭州 310018;
4. 香港浸会大学数学系 香港;
5. 浙江师范大学数学系 金华 321004 |
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| 基金项目： | 国家自然科学基金资助项目（11401535，11371328）；国家留学基金资助项目；香港浸会大学教师研究基金资助项目；浙江省自然科学基金资助项目（LQ15A010010） |
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| 摘 要： | 图G的一个L(2,1)-标号是对G顶点集合的一个非负整数分配,使得其中相邻的点取得的整数差值至少为2并且距离为2的点取得不同的整数.L(2,1)-标号数就是所有这样的标号分配中最小的标号跨度值.Griggs和Yeh的Labelling graphs with a condition at distance 2,SIAM J.Discrete Math.,1992,5:586-595]已经证明了,一棵树的L(2,1)-标号数不是△就是△+1.对于最大度为3的树的L(2,1)-标号数,本文给出了一个完全的刻画.
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| 关 键 词： | L(2 1)-标号 刻画 树 距离2 |
A Characterization of L(2,1)-Labeling Number for Trees with Maximum Degree 3 |
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| Dong CHEN,Wai Chee SHIU,Qiao Jun SHU,Pak Kiu SUN,Wei Fan WANG.A Characterization of L(2,1)-Labeling Number for Trees with Maximum Degree 3[J].Acta Mathematica Sinica,2016,59(5):685-710. |
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| Authors: | Dong CHEN Wai Chee SHIU Qiao Jun SHU Pak Kiu SUN Wei Fan WANG |
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| Institution: | 1. Xingzhi College, Zhejiang Normal University, Jinhua 321004, P. R. China;
2. Department of Mathematics, Hong Kong Baptist University, Hong Kong;
3. School of Science, Hangzhou Dianzi University, Hangzhou 310018, P. R. China;
4. Department of Mathematics, Hong Kong Baptist University, Hong Kong;
5. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| Abstract: | An L(2, 1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive numbers differed by at least 2, and vertices at distance 2 are assigned distinct numbers. The L(2, 1)-labeling number is the minimum range of labels over all such labeling. It was shown by Griggs and YehLabelling graphs with a condition at distance 2, SIAM J. Discrete Math., 1992, 5:586-595] that the L(2,1)-labeling number of a tree is either Δ+1 or Δ+2. We give a complete characterization of L(2, 1)-labeling number for trees with maximum degree 3. |
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| Keywords: | L(2 1)-labelling characterization tree distance two |
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