The L(3,2,1)-Labeling on Bipartite Graphs
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 λ3(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 λ3 for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree T such that λ3(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.
Author Details
Wanlian Yuan Email
Mingqing Zhai Email
Changhong Lü Email