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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 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.

Author Details

Wanlian Yuan

Mingqing Zhai

Changhong Lü