文献类型：期刊文献

中文题名：具有两个度数的树

英文题名：Two-degree trees

作者：乔璞[1];詹兴致[2]

机构：[1]华东理工大学数学学院,上海200237;[2]华东师范大学数学科学学院,上海200241

年份：2023

期号：2

起止页码：1

中文期刊名：华东师范大学学报（自然科学版）

外文期刊名：Journal of East China Normal University(Natural Science)

收录：CSTPCD;;北大核心:【北大核心2020】；CSCD:【CSCD_E2023_2024】；

基金：国家自然科学基金(11671148,11771148);上海市科学技术委员会基金(18dz2271000)。

语种：中文

中文关键词：二度树;直径;唯一图

外文关键词：two-degree tree;diameter;unique graph

摘要：如果一个图只有两个不同的度数,这个图就称为二度图.阶数至少为3的二度树具有度数1和d,这里d是至少为2的整数,这样的树称为(1, d)这些结果提供了一个新的例子,表明有时候图的行为是由数论性质决定的.
A graph is called a two-degree graph if its vertices have only two distinct degrees. A two-degree tree of order at least three have two degrees, 1 and d for some d ≥ 2;such a tree is called a(1, d)-tree.Given a positive integer n, we determine:(1) the possible values of d such that there exists a(1, d)-tree of order n;(2) the values of d such that there exists a unique(1, d)-tree of order n, and(3) the maximum diameter of two-degree trees of order n. The results provide a new example showing that the behavior of graphs may sometimes be determined by number theoretic properties.