{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T12:40:26Z","timestamp":1770640826098,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP.2\/372\/45"],"award-info":[{"award-number":["RGP.2\/372\/45"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The enumeration of spanning trees in various graph forms has been made easier by the study of electrically equivalent transformations, which was motivated by Kirchhoff\u2019s work on electrical networks. In this work, using knowledge of difference equations, the electrically equivalent transformations and rules of weighted generating function are used to calculate the explicit formulas of the number of spanning trees of novel pyramid graph types based on some nonahedral graphs. Lastly, we compare our graphs\u2019 entropy with that of other average-degree graphs that have been researched.<\/jats:p>","DOI":"10.3390\/axioms14030148","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T04:03:17Z","timestamp":1740024197000},"page":"148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Enumerating the Number of Spanning Trees of Pyramid Graphs Based on Some Nonahedral Graphs"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-5943-1290","authenticated-orcid":false,"given":"Ahmad","family":"Asiri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Applied College at Mahail Aseer, King Khalid University, Abha 61421, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3809-2521","authenticated-orcid":false,"given":"Salama Nagy","family":"Daoud","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Nunawara 30001, Saudi Arabia"},{"name":"Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","first-page":"264","article-title":"Asymptotic enumeration theorems for the number of spanning trees and Eulerian trail in circulant digraphs & graphs","volume":"43","author":"Zhang","year":"1999","journal-title":"Sci. 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