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 dG(u,v)=1, |f(u)−f(v)|≥2 if dG(u,v)=2, and |f(u)−f(v)|≥1 if dG(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.