| 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 |
| 圈的$L(d_1,d_2,\ldots,d_t)$-数$\lambda(C_n;d_1,d_2,\ldots,d_t)$ |
| $L(d_1, d_2, \ldots, d_t)$-Number $\lambda(C_n; d_1, d_2, \ldots, d_t)$ of Cycles |
| 投稿时间：2007-07-18 修订日期：2008-04-16 |
| DOI：10.3770/j.issn:1000-341X.2009.04.013 |
| 中文关键词: 圈 $L(d_1,d_2,\ldots,d_t)$-标号 $\lambda(G d_1,d_2,\ldots,d_t)$. |
| 英文关键词:cycle labeling $L(d_1, d_2, \ldots, d_t)$-labeling $\lambda(G d_1, d_2, \ldots, d_t)$-number. |
| 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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| 中文摘要: |
| 图的$L(d_1,d_2,\cdots,d_t)-$标号是一个函数$f$:$V(G)$$\longrightarrow$$\{0,1,2,\cdots\}$,使得若$d(x,y)=i,x,y$$\in$$V(G)$,1$\leq$$i$$\leq$$t$,则$|f(x)-f(y)|$$\geq$$d_i$.图$G$的$L(d_1,d_2,\cdots,d_t)-$数$\lambda(G;d_1,d_2,\cdots,d_t)$}是使得$G$有$L(d_1,d_2,\cdots,d_t)-$标号的最小数.这里得到了$\lambda(C_n;2,2,1)$的精确值,同时,根据圈的特点,给出了$\lambda(C_n;3,2,1)$的上下界,$\lambda(C_n;2,2,\cdots,2,1,1,\cdots,1)$的上下界. |
| 英文摘要: |
| 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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