{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JMN5XPYM/3264015b-8f3a-400f-aaeb-e21fc88116bd/PDF","dcterms:extent":"335 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JMN5XPYM/032ae5e4-e977-4701-a163-cac20e293283/TEXT","dcterms:extent":"41 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-JMN5XPYM","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Nazim, Mohd","Rehman, Nadeem Ur"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"številka:3"},{"@xml:lang":"sl","#text":"P3.05 (16 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2645.8fc","COBISSID_HOST:118098435","ISSN:1855-3966","URN:URN:NBN:SI:doc-JMN5XPYM"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"annihilating-ideal graph"},{"@xml:lang":"en","#text":"complete graph"},{"@xml:lang":"en","#text":"genus of a graph"},{"@xml:lang":"sl","#text":"graf anihilirajočih idealov"},{"@xml:lang":"sl","#text":"graf deliteljev niča"},{"@xml:lang":"en","#text":"planar graph"},{"@xml:lang":"sl","#text":"polni graf"},{"@xml:lang":"sl","#text":"ravninski graf"},{"@xml:lang":"sl","#text":"rod grafa"},{"@xml:lang":"en","#text":"zero-divisor graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the essential annihilating-ideal graph of commutative rings|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$R$? be a commutative ring with unity, ?$A(R)$? be the set of all annihilating-ideals of ?$R$? and ?$A^{\\ast}(R) = A(R) \\setminus \\{0\\}$?. In this paper, we introduced and studied the essential annihilating-ideal graph of ?$R$?, denoted by ?$\\mathcal{EG}(R)$?, with vertex set ?$A^{\\ast}(R)$? and two distinct vertices ?$I_1$? and ?$I_2$? are adjacent if and only if v ?$Ann (I_1 I_2)$? is an essential ideal of ?$R$?. We prove that ?$\\mathcal{EG}(R)$? is a connected graph with diameter at most three and girth at most four if ?$\\mathcal{EG}(R)$? contains a cycle. Furthermore, the rings ?$R$? are characterized for which ?$\\mathcal{EG}(R)$? is a star or a complete graph. Finally, we classify all the Artinian rings ?$R$? for which ?$\\mathcal{EG}(R)$? is isomorphic to some well-known graphs"},{"@xml:lang":"sl","#text":"Naj bo ?$R$? komutativen kolobar z enoto, ?$A(R)$? množica anihilirajočih idealov kolobarja ?$R$? in ?$A^{\\ast}(R) = A(R) \\setminus \\{0\\}$?. V tem članku vpeljemo in preučujemo esencialni graf anihilirajočih idealov kolobarja ?$R$?, označen z ?$\\mathcal{EG}(R)$?; množica njegovih vozlišč je ?$A^{\\ast}(R)$?, dva različna vozlišča ?$I_1$? in ?$I_2$? tega grafa pa sta sosedna če in samo če je ?$Ann (I_1 I_2)$? esencialni ideal kolobarja ?$R$?. Dokažemo, da je ?$\\mathcal{EG}(R)$? povezan graf s premerom največ tri in ožino največ štiri, če ?$\\mathcal{EG}(R)$? vsebuje cikel. Karakteriziramo kolobarje ?$R$?, za katere je ?$\\mathcal{EG}(R)$? zvezda ali pa polni graf. Klasificiramo tudi vse Artinske kolobarje ?$R$?, za katere je ?$\\mathcal{EG}(R)$? izomorfen nekaterim znanim grafom"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-JMN5XPYM","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JMN5XPYM"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JMN5XPYM/3264015b-8f3a-400f-aaeb-e21fc88116bd/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-JMN5XPYM/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JMN5XPYM"}}}}