Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (2): 1-4.doi: 10.3969/j.issn.1000-5641.2023.02.001

• Mathematics •    

Two-degree trees

Pu QIAO1(), Xingzhi ZHAN2,*()   

  1. 1. School of Mathematics, East China University of Science and Technology, Shanghai　200237, China
    2. School of Mathematical Sciences, East China Normal University, Shanghai　200241, China
  • Received:2021-05-07 Online:2023-03-25 Published:2023-03-23
  • Contact: Xingzhi ZHAN E-mail:pq@ecust.edu.cn;zhan@math.ecnu.edu.cn

RichHTML

20

PDF

138

Abstract:

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\geqslant 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.

Key words: two-degree tree, diameter, unique graph

CLC Number: