Counting spanning trees of generalized n-edges Apollonian networks

Gujun Wang () and Feng Zhu
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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

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 09, 1-11

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.

Keywords: Spanning tree; generalized Apollonian networks; Wye-Delta transformation; weighted fans and wheels (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S012918312350119X

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