{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T15:10:19Z","timestamp":1783350619549,"version":"3.54.6"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education in Saudi Arabia","award":["IFP-IMSIU-2023026"],"award-info":[{"award-number":["IFP-IMSIU-2023026"]}]},{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IFP-IMSIU-2023026"],"award-info":[{"award-number":["IFP-IMSIU-2023026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by Sie(\u039b,t), already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph Sie(\u039b,t). In the second step, we extract some degree-based indices of a generalized Sierpinski graph Sie(\u039b,t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph Sie(\u039b,t) by using the Randi\u0107 index.<\/jats:p>","DOI":"10.3390\/axioms12121126","type":"journal-article","created":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T11:26:52Z","timestamp":1702639612000},"page":"1126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Entropy and Multi-Fractal Analysis in Complex Fractal Systems Using Graph Theory"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6765-6595","authenticated-orcid":false,"given":"Zeeshan Saleem","family":"Mufti","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore Campus, Lahore 54600, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali H.","family":"Tedjani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rukhshanda","family":"Anjum","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore Campus, Lahore 54600, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Turki","family":"Alsuraiheed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"ref_1","unstructured":"Gutman, I., Dehmer, M., Zhang, Y., and Ilic, A. 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