{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:22Z","timestamp":1760058742592,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Research and Graduate Studies at King Khalid University","award":["RGP2\/339\/45"],"award-info":[{"award-number":["RGP2\/339\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let \u039b denote a commutative ring with unity and D(\u039b) denote a collection of all annihilating ideals from \u039b. An annihilator intersection graph of \u039b is represented by the notation AIG(\u039b). This graph is not directed in nature, where the vertex set is represented by D(\u039b)*. There is a connection in the form of an edge between two distinct vertices \u03c2 and \u03f1 in AIG(\u039b) iff Ann(\u03c2\u03f1)\u2260Ann(\u03c2)\u2229Ann(\u03f1). In this work, we begin by categorizing commutative rings \u039b, which are finite in structure, so that AIG(\u039b) forms a star graph\/2-outerplanar graph, and we identify the inner vertex number of AIG(\u039b). In addition, a classification of the finite rings where the genus of AIG(\u039b) is 2, meaning AIG(\u039b) is a double-toroidal graph, is also investigated. Further, we determine \u039b, having a crosscap 1 of AIG(\u039b), indicating that AIG(\u039b) is a projective plane. Finally, we examine the domination number for the annihilator intersection graph and demonstrate that it is at maximum, two.<\/jats:p>","DOI":"10.3390\/axioms14050336","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Exploring Geometrical Properties of Annihilator Intersection Graph of Commutative Rings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-3119","authenticated-orcid":false,"given":"Ali Al","family":"Khabyah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1175-9704","authenticated-orcid":false,"given":"Moin A.","family":"Ansari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/0021-8693(88)90202-5","article-title":"Coloring of commutative rings","volume":"116","author":"Beck","year":"1988","journal-title":"J. Algebra"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1006\/jabr.1993.1171","article-title":"Beck\u2019s coloring of a commutative ring","volume":"159","author":"Anderson","year":"1993","journal-title":"J. Algebra"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1006\/jabr.1998.7840","article-title":"The zero-divisor graph of a commutative ring","volume":"217","author":"Anderson","year":"1999","journal-title":"J. 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Graphs, Groups and Surfaces, North-Holland."},{"key":"ref_17","unstructured":"Wisbauer, R. (1991). Foundations of Module and Ring Theory, Breach Science Publishers."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/336\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:22:54Z","timestamp":1760030574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,27]]},"references-count":17,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050336"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050336","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,4,27]]}}}