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Counting spanning trees of generalized n-edges Apollonian networks

Author

Listed:
  • Gujun Wang

    (School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China)

  • Feng Zhu

    (School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China)

Abstract

This paper proposes a generalized form of Apollonian networks and derives their closed expression for the numbers of spanning trees. The n-edges Apollonian networks are transformed into n-order weighted wheels using the electrically equivalent transformations and weighted generating function rules. The numbers of spanning trees in the weighted fans are then calculated to obtain the counting formula of spanning trees in the weighted wheels, thereby deriving the exact expression for spanning trees of the generalized Apollonian networks.

Suggested Citation

  • Gujun Wang & Feng Zhu, 2023. "Counting spanning trees of generalized n-edges Apollonian networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(09), pages 1-11, September.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:09:n:s012918312350119x
    DOI: 10.1142/S012918312350119X
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