{"?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-WXE09X4K/da2d3763-e441-440b-8d05-8f5f8009b712/PDF","dcterms:extent":"308 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-WXE09X4K/b9adec28-cdcd-4cb1-877c-dcb98633f61b/TEXT","dcterms:extent":"29 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-WXE09X4K","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Wang, Xue","Yin, Fu-Gang","Zhou, Jin-Xin"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 325-335"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:44730627","URN:URN:NBN:SI:doc-WXE09X4K"],"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":"automorphism group"},{"@xml:lang":"en","#text":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"sl","#text":"prisekanje"},{"@xml:lang":"en","#text":"truncation"},{"@xml:lang":"en","#text":"vertex-transitive"},{"@xml:lang":"sl","#text":"vozliščna tranzitivnost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On generalized truncations of complete graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"For a ?$k$?-regular graph ?$\\Gamma$? and a graph ?$\\Upsilon$? of order ?$k$?, a generalized truncation of ?$\\Gamma$? by ?$\\Upsilon$? is constructed by replacing each vertex of ?$\\Gamma$? with a copy of ?$\\Upsilon$?. E. Eiben, R. Jajcay and P. Šparl introduced a method for constructing vertex-transitive generalized truncations. For convenience, we call a graph obtained by using Eiben et al.'s method a special generalized truncation. In their paper, Eiben et al. proposed a problem to classify special generalized truncations of a complete graph ?$K_n$? by a cycle of length ?$n-1$?. In this paper, we completely solve this problem by demonstrating that with the exception of ?$n=6$?, every special generalized truncation of a complete graph ?$K_n$? by a cycle of length ?$n-1$? is a Cayley graph of AGL?$(1, n)$? where ?$n$? is a prime power. Moreover, the full automorphism groups of all these graphs and the isomorphisms among them are determined"},{"@xml:lang":"sl","#text":"Za ?$k$?-regularni graf ?$\\Gamma$? in za graf ?$\\Upsilon$? reda ?$k$? definiramo posplošeno prisekanje grafa ?$\\Gamma$? z grafom ?$\\Upsilon$?, tako da vsako vozlišče grafa ?$\\Gamma$? nadomestimo s kopijo grafa ?$\\Upsilon$?. E. Eiben, R. Jajcay in P. Šparl so vpeljali metodo za konstruiranje vozliščno tranzitivnih posplošenih prisekanj. Za potrebe tega članka imenujemo grafe, ki jih dobimo z metodo Eibena et al., posebna posplošena prisekanja. V svojem članku so Eiben et al. postavili problem klasifikacije posebnih posplošenih prisekanj polnega grafa ?$K_n$? s ciklom reda ?$n-1$?. V tem prispevku popolnoma rešimo njihov problem, tako da dokažemo, da je z izjemo ?$n=6$?, vsako posebno prisekanje grafa ?$K_n$? s ciklom reda ?$n-1$? Cayleyjev graf grupe AGL?$(1, n)$?, kjer je ?$n$? potenca praštevila. Poleg tega določimo za vsakega od teh grafov njegovo grupo avtomorfizmov in tudi izomorfizme med njimi"}],"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-WXE09X4K","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-WXE09X4K"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-WXE09X4K/da2d3763-e441-440b-8d05-8f5f8009b712/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-WXE09X4K/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-WXE09X4K"}}}}