{"?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-1MNBF4KI/42b5fda8-9246-49e2-8b86-76e0c2260a1f/PDF","dcterms:extent":"352 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1MNBF4KI/bcf176ae-c9fa-4f64-b909-6876b94c30e0/TEXT","dcterms:extent":"27 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-1MNBF4KI","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":"Stanić, Zoran","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 103-114"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18952793","URN:URN:NBN:SI:doc-1MNBF4KI"],"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":"adjacency matrix"},{"@xml:lang":"sl","#text":"matrika sosednosti"},{"@xml:lang":"en","#text":"net-balanced signed graph"},{"@xml:lang":"sl","#text":"neto-uravnoteženi predznačeni grafi"},{"@xml:lang":"sl","#text":"predznačeni graf"},{"@xml:lang":"sl","#text":"preklopno ekvivalentni predznačeni grafi"},{"@xml:lang":"en","#text":"signed graph"},{"@xml:lang":"en","#text":"switching equivalent signed graphs"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Integral regular net-balanced signed graphs with vertex degree at most four|"},"dc:description":[{"@xml:lang":"sl","#text":"A signed graph is called integral if its spectrum consists entirely of integers, it is ?$r$?-regular if its underlying graph is regular of degree ?$r$?, and it is net-balanced if the difference between positive and negative vertex degree is a constant on the vertex set (this constant is called the net-balance and denoted ?$\\varrho$?). We determine all the connected integral 3-regular net-balanced signed graphs. In the next natural step, for ?$r = 4$?, we consider only those whose net-balance is a simple eigenvalue. There, we complete the list of feasible spectra in bipartite case for ?$\\varrho \\neq 0$? and prove the non-existence for ?$\\varrho = 0$?. Certain existence conditions are established and the existence of some 4-regular (simple) graphs is confirmed. In this study we transferred some results from the theory of graph spectra; in particular, we give a counterpart to the Hoffman polynomial"},{"@xml:lang":"sl","#text":"Predznačeni graf se imenuje celoštevilski, če njegov spekter sestoji izključno iz celih števil, ?$r$?-regularen, če je njegov temeljni graf regularen stopnje ?$r$?, in neto-uravnotežen, če je je razlika med pozitivno in negativno vozliščno stopnjo konstanta na množici vozlišč (ta konstanta, ki jo oznacimo z ?$\\varrho$?, se imenuje neto-uravnoteženost). Določimo vse povezane celoštevilske 3-regularne neto-uravnotežene predznačene grafe. V naslednjem naravnem koraku, za ?$r = 4$?, obravnavamo samo tiste predznačene grafe, katerih neto-uravnoteženost je enostavna lastna vrednost. Pri slednjih dopolnimo seznam dopustnih spektrov v dvodelnem primeru pri ?$\\varrho \\neq 0$? ter dokažemo neobstoj pri ?$\\varrho = 0$?. Dobimo določene eksistenčne pogoje in potrdimo obstoj nekaterih 4-regularnih (enostavnih) grafov. Pri tej raziskavi nekatere rezultate iz spektralne teorije grafov smiselno prenesemo v naš kontekst. Konkretneje, podamo ustrezen analog Hoffmanovemu polinomu"}],"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-1MNBF4KI","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-1MNBF4KI"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-1MNBF4KI/42b5fda8-9246-49e2-8b86-76e0c2260a1f/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-1MNBF4KI/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-1MNBF4KI"}}}}