围长至少为5的平面图的L(p,q)-标号

J4 ›› 2011, Vol. 46 ›› Issue (8): 95-103.

围长至少为5的平面图的L(p,q)-标号

朱海洋¹,侯立峰¹，陈伟1,吕新忠²

1.徐州空军学院后勤指挥系, 江苏徐州 221000; 2. 浙江师范大学数理与信息工程学院, 浙江金华 321004

收稿日期:2010-05-18 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:朱海洋(1979- ),男,硕士,主要研究方向为图论与军事运筹学.Email:tulunzhuhaiyang7@126.com
基金资助:
国家自然科学基金资助项目(10971198)

The L(p,q)-labeling of planar graphs with girth g(G)≥5

ZHU Hai-yang¹, HOU Li-feng¹, CHEN Wei¹, Lü Xin-zhong²

1. Department of Logistics Command, Xuzhou Air Force College, Xuzhou 221000, Jiangsu, China;
2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China

Received:2010-05-18 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

令λ_p,q(G)为图G的L(p,q)标号数,其中p和q是两个正整数且p≥q。证明了若G是围长g(G)≥5的平面图,则λ_p,q(G)≤(2q-1)Δ(G)+6p+10q-8。由此导得对于g(G)≥5且Δ(G)≥16的平面图G,Wegner的猜想成立。

关键词: 平面图;围长;L(p,q)-标号; L(p,q)-标号数

Abstract:

Let p and q be two positive integers with p≥q, and let λ_p,q(G) be the L(p,q)-labeling number of a planar graph G. It is proved that λ_p,q(G)≤(2q-1)Δ(G)+6p+10q-8 if G is a planar graphs with girth g(G)≥5, which implies Wegner’s conjecture holds for a planar graph G with girth g(G)≥5 and Δ(G)≥16.

Key words: planar graph;girth; L(p,q)-labeling; L(p,q)-labeling number

朱海洋1,侯立峰1，陈伟1,吕新忠2. 围长至少为5的平面图的L(p,q)-标号[J]. J4, 2011, 46(8): 95-103.

ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2. The L(p,q)-labeling of planar graphs with girth g(G)≥5[J]. J4, 2011, 46(8): 95-103.

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