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Multi-distance granularity structural α-subtree index of generalized Bethe trees

Author

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  • Yang, Yu
  • Fan, Ai-wan
  • Wang, Hua
  • Lv, Hailian
  • Zhang, Xiao-Dong

Abstract

In graph theory and its applications, trees, BC-trees, subtrees and BC-subtrees have been extensively studied. We introduce a generalization of the BC-tree, called the multi-granular α-tree, which is a tree (of order at least α+1) where any two leaves are at a distance that is a multiple of α. We study the number of α-subtrees, through α-subtree generating functions, for generalized Bethe trees, Bethe trees and dendrimers (hyper-branched structures in molecular topology). Our results can also be used to examine the asymptotic behavior of the average order of α-subtrees in dendrimers.

Suggested Citation

  • Yang, Yu & Fan, Ai-wan & Wang, Hua & Lv, Hailian & Zhang, Xiao-Dong, 2019. "Multi-distance granularity structural α-subtree index of generalized Bethe trees," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 107-120.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:107-120
    DOI: 10.1016/j.amc.2019.04.037
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    References listed on IDEAS

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    1. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    2. Yang, Yu & Liu, Hongbo & Wang, Hua & Fu, Hongsun, 2015. "Subtrees of spiro and polyphenyl hexagonal chains," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 547-560.
    3. Liu, Guoliang & Liu, Guodong, 2018. "Wiener polarity index of dendrimers," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 151-153.
    4. Ghalavand, Ali & Reza Ashrafi, Ali, 2018. "Ordering chemical graphs by Randić and sum-connectivity numbers," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 160-168.
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    Cited by:

    1. Sun, Daoqiang & Li, Long & Liu, Kai & Wang, Hua & Yang, Yu, 2022. "Enumeration of subtrees of planar two-tree networks," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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