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Finding the Number of Spanning Trees in Specific Graph Sequences Generated by a Johnson Skeleton Graph

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Listed:
  • Ahmad Asiri

    (Department of Mathematics, Applied College at Mahail Aseer, King Khalid University, Abha 61421, Saudi Arabia)

  • Salama Nagy Daoud

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Nunawara 41411, Saudi Arabia
    Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt)

Abstract

Using equivalent transformations, complicated circuits in physics that need numerous mathematical operations to analyze can be broken down into simpler equivalent circuits. It is also possible to determine the number of spanning trees—graph families in particular—using these adjustments and utilizing our knowledge of difference equations, electrically equivalent transformations, and weighted generating function rules. In this paper, we derive the exact formulas for the number of spanning trees of sequences of new graph families created by a Johnson skeleton graph 63 and a few of its related graphs. Lastly, a comparison is made between our graphs’ entropy and other graphs of average degree four.

Suggested Citation

  • Ahmad Asiri & Salama Nagy Daoud, 2025. "Finding the Number of Spanning Trees in Specific Graph Sequences Generated by a Johnson Skeleton Graph," Mathematics, MDPI, vol. 13(18), pages 1-35, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:3036-:d:1753918
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