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The L(3,2,1)-Labeling on Bipartite Graphs

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