{"?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-UP6SXFNC/ac9f87e0-5837-4b21-9fc1-8b16b61e584d/PDF","dcterms:extent":"574 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UP6SXFNC/bd1d6717-1e92-4f08-b61e-43a6b211f796/TEXT","dcterms:extent":"74 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UP6SXFNC/50226c12-92ce-419f-b0d3-d36fc7ebe93d/PDF","dcterms:extent":"143 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UP6SXFNC/7c4ceb46-294c-4907-a0e0-f2d3d5baa799/TEXT","dcterms:extent":"4 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-UP6SXFNC","dcterms:issued":"2026","dc:creator":["Aguilar, Flor","Araujo-Pardo, Gabriela","Berman, Leah"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"številka:3, article  p3.03"},{"@xml:lang":"sl","#text":"str. 1-30"}],"dc:identifier":["DOI:10.26493/1855-3974.3116.35e","ISSN:1855-3974","COBISSID_HOST:289872131","URN:URN:NBN:SI:doc-UP6SXFNC"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"en","#text":"girth"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"sl","#text":"napetostni graf"},{"@xml:lang":"sl","#text":"ožina"},{"@xml:lang":"sl","#text":"polkubični graf"},{"@xml:lang":"en","#text":"semicubic graph"},{"@xml:lang":"en","#text":"voltage graph"}],"dc:title":{"@xml:lang":"sl","#text":"Semicubic cages and small graphs of even girth from voltage graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A ({3, m}; g)-semicubic graph is a graph where the degree of each vertex is either 3 or m and the girth of the graph is g; if m = 3 we have a cubic graph. In this paper, we construct families of semicubic graphs of even girth and small order using two different techniques. The first technique generalizes a previous construction, which glues cubic cages of girth g together at remote vertices (vertices at distance at least g/2). The second technique, the main content of this paper, produces bipartite semicubic ({3, m}; g)-graphs of even girth g using voltage graphs over Zm. For girth g = 4t + 2, t ? 1, the constructed graphs have two vertices of degree m. For girth g = 4t, t ? 2, the construction produces graphs with exactly three vertices of degree m (of course, the remaining vertices are of degree 3 in both cases). In particular, we describe infinite families of ({3, m}; g)-semicubic graphs for g = {6, 8, 10, 12} for infinitely many values of m. The cases g = {6, 8} include the unique 6-cage and the unique 8-cage when m = 3. The families obtained in this paper for girth g = {10, 12} include examples of orders that match the best-known bounds for ({3, m}; g)-semicubic graphs until this moment"},{"@xml:lang":"sl","#text":"Graf G imenujemo polkubični ({3, m}; g)-graf, če ima vsako njegovo vozlišče stopnjo bodisi 3 bodisi m, ožina grafa pa je enaka g; za m = 3 dobimo kubični graf. V tem članku konstruiramo družine polkubiˇcnih grafov s sodo ožino in majhnim številom vozlišč z uporabo dveh različnih tehnik. Prva tehnika posplošuje predhodno konstrukcijo, pri kateri se kubične kletke ožine g zlepijo v oddaljenih vozliščih (tj. v vozliščih na medsebojni razdalji vsaj g/2). Druga tehnika, ki predstavlja osrednjo vsebino tega članka, uporablja napetostne grafe nad grupo Zm za konstrukcijo bipartitnih polkubičnih ({3, m}; g)-grafov s sodo ožino g. Za ožino g = 4t + 2, t ? 1, imajo skonstruirani grafi dve vozlišči stopnje m. Za ožino g = 4t, t ? 2, konstrukcija daje grafe z natanko tremi vozlišči stopnje m (v obeh primerih imajo vsa preostala vozlišˇca stopnjo 3). Posebej opišemo neskončne družine polkubičnih ({3, m}; g)-grafov za g ? {6, 8, 10, 12} in neskončno mnogo vrednosti parametra m. Primera g ? {6, 8} vključujeta enolično 6-kletko oziroma enolično 8-kletko, kadar je m = 3. Družine grafov, dobljene v tem članku za ožino g ? {10, 12}, vsebujejo primere z redi, ki dosegajo trenutno najboljše znane meje za polkubične ({3, m}; g)-grafe"}],"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-UP6SXFNC","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-UP6SXFNC"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-UP6SXFNC/ac9f87e0-5837-4b21-9fc1-8b16b61e584d/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-UP6SXFNC/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-UP6SXFNC"}}}}