{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:30:34Z","timestamp":1753882234601,"version":"3.41.2"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"CSIR Emeritus Scientist Scheme of Council of Scientific and Industrial Research","award":["21(1123)\/20\/EMR-II"],"award-info":[{"award-number":["21(1123)\/20\/EMR-II"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p> For a lattice [Formula: see text], we associate a graph called the annihilator intersection graph of [Formula: see text], denoted by [Formula: see text] The vertex set of [Formula: see text] is the set of all nonzero zero-divisors of [Formula: see text] and any two distinct vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text] if and only if [Formula: see text]. It has shown that the [Formula: see text] is disconnected if and only if the number of atoms in [Formula: see text] is two. If [Formula: see text] is connected, then we determine the diameter and the girth of [Formula: see text] We characterize all lattices whose annihilator intersection graph is planar. Further, we obtain the clique number and chromatic number of [Formula: see text] when [Formula: see text] is a finite Boolean lattice. We show that the domination number of [Formula: see text] is not exceeding two. Finally, we obtain a condition under which the annihilator intersection graph is identical with the zero-divisor graph and the annihilator ideal graph of lattices. <\/jats:p>","DOI":"10.1142\/s1793830924500344","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T09:06:34Z","timestamp":1712221594000},"source":"Crossref","is-referenced-by-count":0,"title":["Annihilator intersection graph of a lattice"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1301-2161","authenticated-orcid":false,"given":"Vikas","family":"Kulal","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Engineering and Sciences, MIT Art, Design and Technology University, Pune 412201, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2187-6362","authenticated-orcid":false,"given":"Anil","family":"Khairnar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abasaheb Garware College, Pune 411004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1878-7847","authenticated-orcid":false,"given":"T.","family":"Tamizh Chelvam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,4,27]]},"reference":[{"key":"S1793830924500344BIB001","doi-asserted-by":"publisher","DOI":"10.1515\/gmj-2015-0031"},{"key":"S1793830924500344BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-013-0164-6"},{"key":"S1793830924500344BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-88410-9"},{"key":"S1793830924500344BIB004","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/9825495"},{"issue":"1","key":"S1793830924500344BIB005","first-page":"15","volume":"9","author":"Ebrahimi Atani S.","year":"2018","journal-title":"Categ. 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