Year: 2009
Author: Wanlian Yuan, Mingqing Zhai, Changhong Lü
Communications in Mathematical Research , Vol. 25 (2009), Iss. 1 : pp. 79–87
Abstract
An $L(3, 2, 1)$-labeling of a graph $G$ is a function from the vertex set $V(G)$ to the set of all nonnegative integers such that $|f(u)−f(v)|≥3$ if $d_G(u, v)=1$, $|f(u)−f(v)|≥2$ if $d_G(u, v)=2$, and $|f(u)−f(v)|≥1$ if $d_G(u, v)=3$. The $L(3, 2, 1)$-labeling problem is to find the smallest number $λ_3(G)$ such that there exists an $L(3, 2, 1)$-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of $λ_3$ for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree $T$ such that $λ_3(T)$ attains the minimum value.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CMR-19284
Communications in Mathematical Research , Vol. 25 (2009), Iss. 1 : pp. 79–87
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: channel assignment problems $L(2 1)$-labeling $L(3 2 bipartite graph tree.