(2m＋1，1)-p-树的二分强优美性和二分强奇优美性  

On Bipartite Strongly Gracefulness and Bipartite Strongly Odd-gracefulness of (2m+1,1)-p-trees

作　　者：张明军 赵喜杨 姚兵[2] 

机构地区：[1]兰州财经大学信息工程学院数学系,兰州730020 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《应用数学学报》2016年第3期419-428,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61163054,61163037,61363060);兰州财经大学专项科研经费资助项目

摘　　要：给出了二分优美树和强优美树、强奇优美树、边对称树以及对偶标号的概念,定义了一类(2m+1,1)-p-树.并证明了(2m+1,1)-p-树是二分强优美树和二分强奇优美树,并验证了(2m+1,1)-p-树的优美标号是对偶标号.最后证明了(2m+1,1)-p-树的边对称树仍然是二分驺优美树,并将上面的结论推广到一般情形.This paper presents the concept of trees including bipartite graceful tree, strongly graceful tree, strongly odd-graceful tree, edge symmetric tree and dual labelling and so on. We define the （2m ＋ 1, 1） -p-trees and prove that the tree is bipartite strongly graceful and bipartite strongly odd-graceful. Moreover, we validate the graceful labelling of （2m＋ 1, 1）-p- tree is dual labelling. Finally, we show that the edge symmetric tree of （2m ＋ 1, 1） - p-tree is still bipartite graceful tree..

关 键 词：二分优美树 强优美标号 强奇优美标号 对偶标号 边对称树 

分 类 号：O157.5[理学—数学]