{"?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-8HJJF94N/548a4b3b-b5fd-4272-887c-b28164865205/PDF","dcterms:extent":"279 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-8HJJF94N/3b10a194-50ab-4bd2-b600-6a912b61944c/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-8HJJF94N","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Mednykh, Alexander","Mednykh, Ilya"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"str. 183-192"}],"dc:identifier":["COBISSID:17735513","ISSN:1855-3966","URN:URN:NBN:SI:doc-8HJJF94N"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"sl","#text":"hipereliptičen graf"},{"@xml:lang":"en","#text":"homology group"},{"@xml:lang":"sl","#text":"homološka grupa"},{"@xml:lang":"en","#text":"hyperelliptic graph"},{"@xml:lang":"en","#text":"Riemann--Hurwitz formula"},{"@xml:lang":"sl","#text":"Riemann-Hurwitzeva formula"},{"@xml:lang":"en","#text":"Schreier formula"},{"@xml:lang":"sl","#text":"Schreierjeva formula"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On gamma-hyperellipticity of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"The basic objects of research in this paper are graphs and their branched coverings. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first homology group. A graph is said to be ?$\\gamma$?-hyperelliptic if it is a two fold branched covering of a genus ?$\\gamma$ graph?. The corresponding covering involution is called ?$\\gamma$?-hyperelliptic. The aim of the paper is to provide a few criteria for the involution ?$\\tau$? acting on a graph ?$X$? of genus ?$g$? to be ?$\\gamma$?-hyperelliptic. If $\\tau$ has at least one fixed point then the first criterium states that there is a basis in the homology group ?$H_1(X)$? whose elements are either invertible or split into ?$\\gamma$? interchangeable pairs under the action of ?$\\tau_\\ast$?. The second criterium is given by the formula ?$\\text{tr}_{\\rm{H_1}(X)} (\\tau_\\ast) = 2 \\gamma - g$?. Similar results are also obtained in the case when ?$\\tau$? acts fixed point free"},{"@xml:lang":"sl","#text":"Osnovni objekti raziskave v tem članku so grafi in njihovi razvejani krovi. Graf nam tukaj pomeni okrajšavo za: končen povezan multigraf. Rod grafa je definiran kot red prve homološke grupe. Graf se imenuje ?$\\gamma$?-hipereliptičen, če ga lahko dobimo kot dvolistni razvejani krov nekega grafa roda ?$\\gamma$?. Ustrezni krovni involuciji pravimo ?$\\gamma$?-hipereliptična involucija. Namen članka je najti nekaj kriterijev, ki povedo, kdaj je involucija ?$\\tau$?, delujoča na grafu ?$X$? roda ?$g$?, ?$\\gamma$?-hipereliptična. Če ima ?$\\tau$? vsaj eno fiksno točko, potem prvi kriterij pove, da obstaja baza v homološki grupi ?$H_1(X)$)?, katere elementi so bodisi obrnljivi bodisi se razcepijo v ?$\\gamma$?-izmenljive pare pod delovanjem ?$\\tau_\\ast$?. Drugi kriterij je dan s formulo ?$\\text{tr}_{\\rm{H_1}(X)} (\\tau_\\ast) = 2 \\gamma - g$?. Podobne rezultate dobimo tudi v primeru, ko ?$\\tau$? deluje brez fiksnih točk"}],"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-8HJJF94N","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-8HJJF94N"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-8HJJF94N/548a4b3b-b5fd-4272-887c-b28164865205/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-8HJJF94N/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-8HJJF94N"}}}}