{"?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-7X6N4EDQ/3f1d72d0-adf9-421a-96fe-3cc2d3770481/PDF","dcterms:extent":"372 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7X6N4EDQ/bcfc8567-03ba-4fd0-9dad-d52ef663ed1d/TEXT","dcterms:extent":"41 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7X6N4EDQ/04b3789a-8f08-46c6-8023-9f893d646089/PDF","dcterms:extent":"132 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7X6N4EDQ/e18cf5a9-c5c9-4ba0-81dd-c970047a2f6d/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-7X6N4EDQ","dcterms:issued":"2025","dc:creator":"Damnjanović, Ivan","dc:format":[{"@xml:lang":"sl","#text":"letnik:1"},{"@xml:lang":"sl","#text":"številka:1, article   p1.04"},{"@xml:lang":"sl","#text":"str. 1-16"}],"dc:identifier":["DOI:10.26493/2820-6657.6.5a1","ISSN:2820-6657","COBISSID_HOST:285423363","URN:URN:NBN:SI:doc-7X6N4EDQ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"University of Primorska"},"dc:source":{"@xml:lang":"sl","#text":"Discrete mathematical chemistry"},"dc:subject":[{"@xml:lang":"en","#text":"adjacency matrix"},{"@xml:lang":"en","#text":"circulant graph"},{"@xml:lang":"sl","#text":"cirkulantni graf"},{"@xml:lang":"sl","#text":"kvartični graf"},{"@xml:lang":"sl","#text":"ničelni prostor"},{"@xml:lang":"en","#text":"null space"},{"@xml:lang":"en","#text":"nut graph"},{"@xml:lang":"sl","#text":"orešni graf"},{"@xml:lang":"en","#text":"quartic graph"},{"@xml:lang":"en","#text":"singular graph"},{"@xml:lang":"sl","#text":"singularni graf"},{"@xml:lang":"sl","#text":"sosednostna matrika"}],"dc:title":{"@xml:lang":"sl","#text":"On the null spaces of quartic circulant graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A nut graph is a nontrivial simple graph whose adjacency matrix has a one-dimensionalnull space such that its nonzero vectors contain no zero elements. For circulant graphs, itis known that they are nut if and only if their nullity is one. This fact was recently usedby the author in order to show that there exists ad-regular circulant nut graph of order n if and only if 4|d,2|n, d >0, alongside n ?d+ 4 if d?84, and n ?d+ 6 if 8|d, and (n, d)?= (16,8). Here, we deal with the quartic circulant graphs and disclose several results regarding their null spaces. First of all, we derive an explicit formula for computing the nullity of any quartic circulant graph. Furthermore, we provide the full nut graph characterization among these graphs. Finally, we determine all such graphs that attain the minimum or maximum nullity with respect to a given order. We also give the extremal null spaces of these graphs"},{"@xml:lang":"sl","#text":"Orešni graf je netrivialen enostaven graf, katerega sosednostna matrika ima enodimenzionalni ničelni prostor, pri čemer noben od njegovih neničelnih vektorjev ne vsebuje ničelnih elementov. Za cirkulantne grafe je znano, da so orešni grafi natanko tedaj, ko je njihova ničelnost ena. Ta dejstvo je avtor nedavno uporabil za dokaz, da obstaja d-regularen cirkulantni orešni graf reda n natanko tedaj, ko 4|d,2|n, d >0, skupaj z n?d+ 4 če d?8 4, in n?d+ 6 če 8|d, ter (n, d)?= (16,8). V tem delu se ukvarjamo s kvartičnimi cirkulantnimi grafi in razkrivamo več rezultatov glede njihovih ničelnih prostorov. Najprej izpeljemo eksplicitno formulo za izračun ničelnosti kateregakoli kvartičnega cirkulantnega grafa. Nadalje podamo popolno karakterizacijo orešnih grafov med temi grafi. Nazadnje določimo vse take grafe, ki dosegajo minimalno ali maksimalno ničelnost glede na dano velikost. Prav tako podajamo ekstremalne ničelne prostore teh grafov"}],"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-7X6N4EDQ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7X6N4EDQ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7X6N4EDQ/3f1d72d0-adf9-421a-96fe-3cc2d3770481/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by-sa/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"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-7X6N4EDQ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7X6N4EDQ"}}}}