探讨奇优美树猜想

J4 ›› 2012, Vol. 47 ›› Issue (12): 31-36.

探讨奇优美树猜想

周向前，姚兵*，陈祥恩

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2011-01-03 出版日期:2012-12-20 发布日期:2012-12-14
通讯作者: 姚兵(1956- ), 男, 副教授, 研究方向为图的着色、标号和复杂网络. Email: yybb918@163.com
作者简介:周向前(1983- ), 男, 硕士研究生, 研究方向为图的着色和标号. Email: zhouxiangqian0502@126.com
基金资助:
国家自然科学基金资助项目(61163054,61163037)

iscuss odd-graceful trees conjecture

ZHOU Xiang-qian, YAO Bing*, CHEN Xiang-en

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2011-01-03 Online:2012-12-20 Published:2012-12-14

摘要/Abstract

摘要：

给出了二分奇优美树和强奇优美树的概念,证明了一棵树是二分奇优美的当且仅当它是二分优美的。还给出了一些构造奇优美树的方法,并证明了:对任意给定的正整数m,如果蜘蛛树T的每条腿长为m或m+1,则T是奇优美树。得到了一些构造奇优美树的快速方法。

关键词: 奇优美标号;强奇优美树;(强)二分奇优美树

Abstract:

Two new labelings related to the odd-graceful problem are introduced. A necessary and sufficient condition between a bipartite odd-graceful tree and a bipartite graceful tree is shown. Several constructive methods for constructing large scale of odd-graceful trees are determined. It has been shown that a spider, each of leg which has length in ｛m,m+1｝ for m≥1, is odd-graceful.

Key words: odd-graceful labeling; strongly odd-graceful trees; (strongly) bipartite odd-graceful trees

周向前，姚兵*，陈祥恩. 探讨奇优美树猜想[J]. J4, 2012, 47(12): 31-36.

ZHOU Xiang-qian, YAO Bing*, CHEN Xiang-en. iscuss odd-graceful trees conjecture[J]. J4, 2012, 47(12): 31-36.

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