{"?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-2IC0BDX5/2d1957f2-9e2b-49e6-a2dc-75b04f73c6de/PDF","dcterms:extent":"428 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-2IC0BDX5/cecd4830-57a7-4ffc-be6d-9f8461acf0aa/TEXT","dcterms:extent":"46 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-2IC0BDX5/7785dc17-d7d7-4d79-916c-c9a08a533668/PDF","dcterms:extent":"129 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-2IC0BDX5/6a87f7d5-fc54-40c2-bc64-22df3a14ccd7/TEXT","dcterms:extent":"3 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-2IC0BDX5","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":"Mirafzal, Seyed Morteza","dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P2.06 (16 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2621.26f","COBISSID_HOST:151635459","ISSN:1855-3966","URN:URN:NBN:SI:doc-2IC0BDX5"],"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":"automorphic graph"},{"@xml:lang":"en","#text":"automorphism group"},{"@xml:lang":"sl","#text":"avtomorfni graf"},{"@xml:lang":"en","#text":"distance-transitive graph"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"sl","#text":"hiperkocka"},{"@xml:lang":"en","#text":"hypercube"},{"@xml:lang":"en","#text":"Johnson graph"},{"@xml:lang":"sl","#text":"Johnsonov graf"},{"@xml:lang":"sl","#text":"kvadrat grafa"},{"@xml:lang":"sl","#text":"razdaljno tranzitiven graf"},{"@xml:lang":"en","#text":"square of a graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Some remarks on the square graph of the hypercube|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$\\Gamma = (V, E)$? be a graph. The square graph ?$\\Gamma^2$? of the graph ?$\\Gamma$? is the graph with the vertex set ?$V (\\Gamma^2) = V$? in which two vertices are adjacent if and only if their distance in ?$\\Gamma$? is at most two. An interesting property of the square graph of the hypercube ?$Q_n$? is that it is highly symmetric and panconnected. In this article, the author investigates some algebraic properties of the graph ?$Q^2_n$?. He shows that the graph ?$Q^2_n$? is distance-transitive and that the graph ?$Q^2_n$? is an imprimitive distance-transitive graph if and only if ?$n$? is an odd integer and determines the spectrum of the graph ?$Q^2_n$?. Finally, the author shows that when ?$n > 2$? is an even integer, then ?$Q^2_n$? is an automorphic graph, that is, ?$Q^2_n$? is a distance-transitive primitive graph which is not a complete or a line graph"},{"@xml:lang":"sl","#text":"Naj bo ?$\\Gamma = (V, E)$? graf. Kvadratni graf ?$\\Gamma^2$? grafa ?$\\Gamma$? je graf z množico vozlišč ?$V (\\Gamma^2) = V$?, v katerem sta dve vozlišči sosednji, če je njuna razdalja v grafu ?$\\Gamma$? največ dve. Kvadratni graf hiperkocke ?$Q_n$? ima določene zanimive lastnosti. Tako je npr. visoko simetričen in vsepovezan. V tem članku raziskujemo nekatere algebraične lastnosti grafa ?$Q^2_n$?. V prvi vrsti pokažemo, da je graf ?$Q^2_n$? razdaljno tranzitiven. Dokažemo tudi, da je graf ?$Q^2_n$? neprimitiven razdaljno tranzitiven graf natanko takrat, ko je ?$n$? sodo število. Določimo tudi spekter grafa ?$Q^2_n$?. Nazadnje dokažemo: če je ?$n > 2$? sodo število, potem je ?$Q^2_n$? avtomorfen graf, kar pomeni, da je ?$Q^2_n$? razdaljno tranzitiven primitiven graf, ki ni ne polni ne povezavni graf"}],"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-2IC0BDX5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-2IC0BDX5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-2IC0BDX5/2d1957f2-9e2b-49e6-a2dc-75b04f73c6de/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-2IC0BDX5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-2IC0BDX5"}}}}