| 圈的$L(d_1,d_2,\ldots,d_t)$-数$\lambda(C_n;d_1,d_2,\ldots,d_t)$ |
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| 引用本文： | 高振滨,张晓东.圈的$L(d_1,d_2,\ldots,d_t)$-数$\lambda(C_n;d_1,d_2,\ldots,d_t)$[J].数学研究及应用,2009,29(4):682-686. |
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| 作者姓名： | 高振滨 张晓东 |
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| 作者单位： | 哈尔滨工程大学理学院, 黑龙江 哈尔滨 150001;上海交通大学数学系, 上海 200240 |
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| 基金项目： | 国家自然科学基金(No.10531070); 国家重点基础研究发展计划(973计划); 上海市自然科学基金(No.06ZR14049). |
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| 摘 要： | An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L（d1,d2,...,dt）-number λ（G;d1,d2,... ,dt） of G is the smallest integer number k such that G has an L（d1,d2,...,dr）- labeling with max{f （x）｜x ∈ V（G）} = k. In this paper, we obtain the exact values for λ（Cn; 2, 2, 1） and λ（Cn; 3, 2, 1）, and present lower and upper bounds for λ（Cn; 2,..., 2, 1,..., 1）
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| 关 键 词： | DT公司 Cn空间 周期 顶点集 函数 MAX 标记 整数 |
| 收稿时间： | 2007/7/18 0:00:00 |
| 修稿时间： | 2008/4/16 0:00:00 |
$L(d_1, d_2, \ldots, d_t)$-Number $\lambda(C_n; d_1, d_2, \ldots, d_t)$ of Cycles |
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| GAO Zhen Bin and ZHANG Xiao Dong.$L(d_1, d_2, \ldots, d_t)$-Number $\lambda(C_n; d_1, d_2, \ldots, d_t)$ of Cycles[J].Journal of Mathematical Research with Applications,2009,29(4):682-686. |
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| Authors: | GAO Zhen Bin and ZHANG Xiao Dong |
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| Institution: | College of Science, Harbin Engineering University, Heilongjiang 150001, China;Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Abstract: | An $L(d_1, d_2, \ldots, d_t)$-labeling of a graph $G$ is a function $f$ from its vertex set $V(G)$ to the set $\{0, 1, \ldots, k\}$ for some positive integer $k$ such that $|f(x)-f(y)|\geq d_i$, if the distance between vertices $x$ and $y$ in $G$ is equal to $i$ for $i=1, 2, \ldots, t$. The $L(d_1, d_2, \ldots, d_t)$-number $\lambda(G; d_1, d_2, \ldots, d_t)$ of $G$ is the smallest integer number $k$ such that $G$ has an $L(d_1, d_2, \ldots, d_t)$-labeling with $\max\{f(x)| x\in V(G)\}=k$. In this paper, we obtain the exact values for $\lambda(C_n; 2, 2, 1)$ and $\lambda(C_n; 3, 2, 1)$, and present lower and upper bounds for $\lambda(C_n; 2,\ldots, 2, 1, \ldots, 1)$ |
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| Keywords: | cycle labeling $L(d_1 d_2 \ldots d_t)$-labeling $\lambda(G d_1 d_2 \ldots d_t)$-number |
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