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

Ahmad Asiri and Salama Nagy Daoud ()
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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

Mathematics, 2025, vol. 13, issue 18, 1-35

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.

Keywords: number of spanning trees; electrically equivalent transformations; entropy; graph sequence Johnson skeleton graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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