{"?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-BJRX7J58/4d7dc3bd-2102-425a-b4d2-36326a88d237/PDF","dcterms:extent":"262 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-BJRX7J58/08733c93-0512-47a3-b116-bfebc9307821/TEXT","dcterms:extent":"25 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-BJRX7J58","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Alspach, Brian","Dobson, Edward"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 215-223"}],"dc:identifier":["COBISSID:17371225","ISSN:1855-3966","URN:URN:NBN:SI:doc-BJRX7J58"],"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":"en","#text":"Hamiltonian"},{"@xml:lang":"sl","#text":"Hamiltonov graf"},{"@xml:lang":"sl","#text":"prisekanje"},{"@xml:lang":"sl","#text":"skoraj-uniformne družine delnih vsot"},{"@xml:lang":"en","#text":"truncation"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On automorphism groups of graph truncations|"},"dc:description":[{"@xml:lang":"sl","#text":"It is well known that the Petersen graph, the Coxeter graph, as well as the graphs obtained from these two graphs by replacing each vertex with a triangle, are trivalent vertex-transitive graphs without Hamilton cycles, and are indeed the only known connected vertex-transitive graphs of valency at least two without Hamilton cycles. It is known by many that the replacement of a vertex with a triangle in a trivalent vertex-transitive graph results in a vertex-transitive graph if and only if the original graph is also arc-transitive. In this paper, we generalize this notion to ?$t$?-regular graphs ?$\\Gamma$? and replace each vertex with a complete graph ?$K_t$? on ?$t$? vertices. We determine necessary and sufficient conditions for ?$\\mathscr{T}(\\Gamma)$? to be hamiltonian, show ?$\\text{Aut}(\\mathscr{T}(\\Gamma)) \\cong \\text{Aut}(\\Gamma)$?, as well as show that if ?$\\Gamma$? is vertex-transitive, then ?$\\mathscr{T}(\\Gamma)$? is vertex-transitive if and only if ?$\\Gamma$? is arc-transitive. Finally, in the case where ?$t$? is prime we determine necessary and sufficient conditions for ?$\\mathscr{T}(\\Gamma)$? to be isomorphic to a Cayley graph as well as an additional necessary and sufficient condition for ?$\\mathscr{T}(\\Gamma)$? to be vertex-transitive"},{"@xml:lang":"sl","#text":"Znano je, da so Petersenov graf, Coxeterjev graf, pa tudi grafi, dobljeni iz njiju z nadomestitvijo vsakega vozlišča s trikotnikom, trivalentni vozliščno-tranzitivni grafi brez Hamiltonovih ciklov; to so tudi edini znani povezani vozlično-tranzitivni grafi valence najmanj dve brez Hamiltonovih ciklov. Znano je tudi, da zamenjava vozlišča s trikotnikom v trivalentnem vozliščno-tranzitivnem grafu da vozliščno-tranzitiven graf če in samo če je prvotni graf tudi ločno-tranzitiven. V tem članku posplošimo ta koncept na ?$t$?-regularne grafe ?$\\Gamma$? in nadomestimo vsako vozlišče s polnim grafom ?$K_t$? na ?$t$? vozliščih. Določimo potrebne in zadostne pogoje za to, da je ?$\\mathscr{T}(\\Gamma)$? hamiltonski, pokažemo, da je ?$\\text{Aut}(\\mathscr{T}(\\Gamma)) \\cong \\text{Aut}(\\Gamma)$?, pokažemo pa tudi, da če je ?$\\Gamma$? vozliščno-tranzitiven, potem je ?$\\mathscr{T}(\\Gamma)$? vozliščno-tranzitiven, če in samo če je ?$\\Gamma$? ločno-tranzitiven. V primeru, ko je ?$t$? praštevilo, določimo potrebne in zadostne pogoje za to, da je ?$\\mathscr{T}(\\Gamma)$? izomorfen Cayleyevemu grafu, pa tudi dodaten potreben in zadosten pogoj za to, da je ?$\\mathscr{T}(\\Gamma)$? vozliščno-tranzitiven"}],"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-BJRX7J58","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-BJRX7J58"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-BJRX7J58/4d7dc3bd-2102-425a-b4d2-36326a88d237/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-BJRX7J58/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-BJRX7J58"}}}}