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Algorithms for enumerating multiple leaf-distance granular regular α-subtree of unicyclic and edge-disjoint bicyclic graphs

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Listed:
  • Li, Long
  • Yang, Yu
  • Hui, Zhi-hao
  • Jin, Bang-Bang
  • Wang, Hua
  • Fahad, Asfand
  • Zhang, Heng

Abstract

A multiple leaf-distance granular regular α-tree (abbreviated as LDR α-tree for short) is a tree (with at least α+1 vertices) where any two leaves are at some distance divisible by α. A connected graph's subtree which is additionally an LDR α-tree is known as an LDR α-subtree. Obviously, α=1 and 2, correspond to the general subtrees (excluding the single vertex subtrees) and the BC-subtrees (the distance between any two leaves of the subtree is even), respectively. With generating functions and structure decomposition, in this paper, we propose algorithms for enumerating an auxiliary subtree ατ(v)-subtree (τ=0,1,…,α−1) containing a fixed vertex, and various LDR α-subtrees of unicyclic graphs, respectively. Basing on these algorithms, we further present algorithms for enumerating various LDR α-subtrees of edge-disjoint bicyclic graphs.

Suggested Citation

  • Li, Long & Yang, Yu & Hui, Zhi-hao & Jin, Bang-Bang & Wang, Hua & Fahad, Asfand & Zhang, Heng, 2024. "Algorithms for enumerating multiple leaf-distance granular regular α-subtree of unicyclic and edge-disjoint bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005039
    DOI: 10.1016/j.amc.2023.128334
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    References listed on IDEAS

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    1. Dale R. Fox, 1988. "Block cutpoint decomposition for markovian queueing systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 4(2), pages 101-114, June.
    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.
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