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 • Next Articles
Pu QIAO1(), Xingzhi ZHAN2,*()
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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:
O157.5
Pu QIAO, Xingzhi ZHAN. Two-degree trees[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 1-4.
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https://xblk.ecnu.edu.cn/EN/Y2023/V2023/I2/1
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