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We take into consideration the ring [Formula: see text] for [Formula: see text] where [Formula: see text] and [Formula: see text] are distinct prime numbers. Moreover, we also discussed the entropy measure of the zero-divisor graph for the rings [Formula: see text] and [Formula: see text] This study will help us further understand the algebraic structure of the commutative rings. <\/jats:p>","DOI":"10.1142\/s1793830923501045","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T03:04:05Z","timestamp":1702350245000},"source":"Crossref","is-referenced-by-count":2,"title":["On degree-based entropy measure for zero-divisor graphs"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2439-3967","authenticated-orcid":false,"given":"Muhammad Farhan","family":"Hanif","sequence":"first","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7325-5586","authenticated-orcid":false,"given":"Hasan","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan"},{"name":"Department of Mathematics, Government College University, Lahore, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9901-0924","authenticated-orcid":false,"given":"Shahbaz","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2024,1,6]]},"reference":[{"issue":"2","key":"S1793830923501045BIB001","first-page":"65","volume":"81","author":"Ahmad A.","year":"2019","journal-title":"Politeh. 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