$L(d_1, d_2, \ldots, d_t)$-Number $\lambda(C_n; d_1, d_2, \ldots, d_t)$ of Cycles
Received:July 18, 2007  Revised:April 16, 2008
Key Words: cycle   labeling   $L(d_1, d_2, \ldots, d_t)$-labeling   $\lambda(G   d_1, d_2, \ldots, d_t)$-number.  
Fund Project:the National Natural Science Foundation of China (No.10531070); the National Basic Research Program of China 973 Program (No.2006AA11Z209) and the Natural Science Foundation of Shanghai City (No.06ZR14049).
Author NameAffiliation
GAO Zhen Bin College of Science, Harbin Engineering University, Heilongjiang 150001, China 
ZHANG Xiao Dong Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China 
Hits: 3286
Download times: 2044
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 $\lambda(C_n; 2,\ldots, 2, 1, \ldots, 1)$
Citation:
DOI:10.3770/j.issn:1000-341X.2009.04.013
View Full Text  View/Add Comment