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In this paper, we determine the diameter, girth of [Formula: see text]. Specifically, we classify all finite commutative nonlocal rings for which [Formula: see text] is perfect. Furthermore, we discuss about the planarity, outerplanarity, genus and crosscap of [Formula: see text] and characterize all of them.<\/jats:p>","DOI":"10.1142\/s1793830922501907","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T13:36:35Z","timestamp":1670420195000},"source":"Crossref","is-referenced-by-count":2,"title":["On the ideal-based zero-divisor graph of commutative rings"],"prefix":"10.1142","volume":"16","author":[{"given":"K.","family":"Selvakumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu 627012, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.","family":"Anusha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu 627012, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2023,1,21]]},"reference":[{"key":"S1793830922501907BIB001","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0021-8693(03)00370-3","volume":"270","author":"Akbari S.","year":"2003","journal-title":"J. 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