探讨奇优美树猜想  

Discuss odd-graceful trees conjecture

作　　者：周向前[1] 姚兵[1] 陈祥恩[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2012年第12期31-36,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61163054;61163037)

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。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.

关 键 词：奇优美标号 强奇优美树 (强)二分奇优美树 

分 类 号：O157.5[理学—数学]