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Subtrees of spiro and polyphenyl hexagonal chains

Author

Listed:
  • Yang, Yu
  • Liu, Hongbo
  • Wang, Hua
  • Fu, Hongsun

Abstract

The number of subtrees of a graph and its variations are among popular topological indices that have been vigorously studied. We investigate the subtree numbers of spiro and polyphenyl hexagonal chains, molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. We first present the generating functions for subtrees, through which explicit formulas for computing the subtree number of spiro and polyphenyl hexagonal chains are obtained. We then establish a relation between the subtree numbers of a spiro hexagonal chain and its corresponding polyphenyl hexagonal chain. This allows us to show that the spiro and polyphenyl hexagonal chains with the minimum (resp. second minimum, third minimum) subtree numbers coincide with the ones that attain the maximum (resp. second maximum, third maximum) Wiener indices, and vice versa. The subtree densities of these hexagonal chains are also briefly discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:547-560
    DOI: 10.1016/j.amc.2015.06.094
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    References listed on IDEAS

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    1. Dehmer, Matthias & Shi, Yongtang & Mowshowitz, Abbe, 2015. "Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 352-355.
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    Cited by:

    1. 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).
    2. Chen, Ailian & Xiong, Xianzhu & Lin, Fenggen, 2016. "Distance-based topological indices of the tree-like polyphenyl systems," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 233-242.
    3. Yu Yang & An Wang & Hua Wang & Wei-Ting Zhao & Dao-Qiang Sun, 2019. "On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    4. 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.

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