{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:24:08Z","timestamp":1753885448656,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"Mathematical Research Impact Centric Support","award":["DST [MTR\/2018\/000607]"],"award-info":[{"award-number":["DST [MTR\/2018\/000607]"]}]},{"name":"University Grant Commission for the rese","award":["CSIR-UGC NET JUNE 2017"],"award-info":[{"award-number":["CSIR-UGC NET JUNE 2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> The concept of associating a graph to a ring was initiated by Beck in 1988. The zero-divisor graph of a commutative ring [Formula: see text] with unity ([Formula: see text]) is defined as a simple graph, denoted by [Formula: see text], where elements of the ring [Formula: see text] represent vertices and two distinct vertices in [Formula: see text] are adjacent if the product of the corresponding elements is zero in [Formula: see text]. Here, we extend the notion of zero-divisor graphs to signed graphs. We introduce four types of signing to the zero-divisor graphs. Further, we characterize rings for which these four types of signed graphs, its lined signed graphs and their negations are balanced, clusterable, sign-compatible, canonically sign-compatible, and canonically consistent. <\/jats:p>","DOI":"10.1142\/s179383092250135x","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T04:19:30Z","timestamp":1660709970000},"source":"Crossref","is-referenced-by-count":0,"title":["Properties of derived signed graphs on Beck\u2019s zero-divisor graph"],"prefix":"10.1142","volume":"15","author":[{"given":"Bableen","family":"Kaur","sequence":"first","affiliation":[{"name":"Department of Mathematics, South Asian University, 110021, New Delhi, India"}]},{"given":"Deepa","family":"Sinha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Asian University, 110021, New Delhi, India"}]}],"member":"219","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"issue":"12","key":"S179383092250135XBIB001","first-page":"431","volume":"6","author":"Acharya B. D.","year":"1983","journal-title":"Nat. Acad. Sci. Lett."},{"issue":"6","key":"S179383092250135XBIB002","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1080\/09720529.2010.10698314","volume":"13","author":"Acharya B. D.","year":"2010","journal-title":"J. Discrete Math. Sci. Cryptogr."},{"issue":"2","key":"S179383092250135XBIB003","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1006\/jabr.1993.1171","volume":"159","author":"Anderson D. D.","year":"1993","journal-title":"J. Algebra"},{"key":"S179383092250135XBIB004","first-page":"61","volume":"220","author":"Anderson D. F.","year":"1999","journal-title":"Lecture Notes Pure Appl. Math."},{"issue":"2","key":"S179383092250135XBIB005","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1006\/jabr.1998.7840","volume":"217","author":"Anderson D. F.","year":"1999","journal-title":"J. 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A.","year":"1967","journal-title":"Human Relations"},{"key":"S179383092250135XBIB010","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"issue":"2","key":"S179383092250135XBIB011","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1307\/mmj\/1028989917","volume":"2","author":"Harary F.","year":"1953","journal-title":"Michigan Math. J."},{"volume-title":"Commutative Rings","year":"1974","author":"Kaplansky I.","key":"S179383092250135XBIB012"},{"issue":"2","key":"S179383092250135XBIB013","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1081\/AGB-120013178","volume":"30","author":"Levy R.","year":"2002","journal-title":"Comm. Algebra"},{"issue":"7","key":"S179383092250135XBIB014","doi-asserted-by":"crossref","first-page":"3533","DOI":"10.1081\/AGB-120004502","volume":"30","author":"Mulay S. B.","year":"2002","journal-title":"Comm. 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