| 树的L(3,2,1)-标号问题 |
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| 引用本文： | 张小玲.树的L(3,2,1)-标号问题[J].数学研究及应用,2020,40(5):467-475. |
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| 作者姓名： | 张小玲 |
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| 作者单位： | 泉州师范学院数学与计算机科学学院, 福建 泉州 362000 |
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| 基金项目： | 国家自然科学基金青年科学基金项目(Grant No.11601265),泉州市高层次人才项目(Grant No.2017Z033). |
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| 摘 要： | An L(3,2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers(labels) such that |f(u)-f(v)|≥3 if d(u,v)=1,|f(u)-f(v)≥2 if d(u,v)=2 and |f(u)-f(v)|≥1 if d(u,v)=3.For a non-negative integer k,a k-L(3,2,1)-labeling is an L(3,2,1)-labeling such that no label is greater than k.The L(3,2,1)-labeling number of G,denoted by λ_(3,2,1)(G), is the smallest number k such that G has a k-L(3,2,1)-labeling.In this article,we characterize the L(3,2,1)-labeling numbers of trees with diameter at most 6.
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| 关 键 词： | 频率分配 $L(3 2 1)$-标号 树 直径 |
| 收稿时间： | 2019/7/29 0:00:00 |
| 修稿时间： | 2020/3/17 0:00:00 |
The $L(3,2,1)$-Labeling Problem for Trees |
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| Xiaoling ZHANG.The $L(3,2,1)$-Labeling Problem for Trees[J].Journal of Mathematical Research with Applications,2020,40(5):467-475. |
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| Authors: | Xiaoling ZHANG |
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| Institution: | College of Mathematics and Computer Science, Quanzhou Normal University, Fujian 362000, P. R. China |
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| Abstract: | An $L(3,2,1)$-labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all non-negative integers (labels) such that $|f(u)-f(v)| \geq 3$ if $d(u, v) = 1$, $|f(u) - f(v)| \geq 2$ if $d(u, v) = 2$ and $|f(u)-f(v)| \geq 1$ if $d(u, v) = 3$. For a non-negative integer $k$, a $k$-$L(3,2,1)$-labeling is an $L(3,2,1)$-labeling such that no label is greater than $k$. The $L(3,2,1)$-labeling number of $G$, denoted by $\lambda_{3,2,1}(G)$, is the smallest number $k$ such that $G$ has a $k$-$L(3,2,1)$-labeling. In this article, we characterize the $L(3, 2, 1)$-labeling numbers of trees with diameter at most 6. |
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| Keywords: | channel assignment $L(3 2 1)$-labeling trees diameter |
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