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On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

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  • Yu Yang

    (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
    School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

  • An Wang

    (School of Mathematics and Statistics Science, Pingdingshan University, Pingdingshan 467000, China)

  • Hua Wang

    (College of Software, Nankai University, Tianjin 300071, China
    Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA)

  • Wei-Ting Zhao

    (School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

  • Dao-Qiang Sun

    (School of Computer Science, Pingdingshan University, Pingdingshan 467000, China)

Abstract

The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal problems in the corresponding class of graphs. Some interesting observations on the behavior of the subtree number are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:472-:d:234190
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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. 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.
    3. 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.
    4. Zetina, Carlos Armando & Contreras, Ivan & Fernández, Elena & Luna-Mota, Carlos, 2019. "Solving the optimum communication spanning tree problem," European Journal of Operational Research, Elsevier, vol. 273(1), pages 108-117.
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