{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:24:38Z","timestamp":1773260678445,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"University Grants Commission","award":["F.42- 8\/2013(SR)"],"award-info":[{"award-number":["F.42- 8\/2013(SR)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with identity. We consider a simple graph associated with [Formula: see text], denoted by [Formula: see text], whose vertex set is the set of all non-trivial ideals of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text] or [Formula: see text]. In this paper, we characterize the commutative Artinian non-local ring [Formula: see text] for which [Formula: see text] has genus one and crosscap one. <\/jats:p>","DOI":"10.1142\/s1793830917500586","type":"journal-article","created":{"date-parts":[[2017,7,19]],"date-time":"2017-07-19T06:44:00Z","timestamp":1500446640000},"page":"1750058","source":"Crossref","is-referenced-by-count":5,"title":["On the genus of the graph associated to a commutative ring"],"prefix":"10.1142","volume":"09","author":[{"given":"K.","family":"Selvakumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India"}]},{"given":"P.","family":"Subbulakshmi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India"}]},{"given":"Jafar","family":"Amjadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. 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