{"?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-9Q5KSCI1/129db946-1582-49fd-9eb8-b414148641e5/PDF","dcterms:extent":"485 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-9Q5KSCI1/591e424f-4284-4129-a4a0-ec2c06f5b7ab/TEXT","dcterms:extent":"45 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-9Q5KSCI1/760080bc-cb24-4dcd-a8d4-70e810f157b9/PDF","dcterms:extent":"205 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-9Q5KSCI1/a92c172b-cf9a-4529-8751-fd4498c02431/TEXT","dcterms:extent":"3 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-9Q5KSCI1","dcterms:issued":"2025","dc:creator":["Imrich, Wilfried","Kalinowski, Rafał","Pilśniak, Monika"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1, article  p1.06"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 1-17"}],"dc:identifier":["DOI:10.26493/2590-9770.1701.10e","ISSN:2590-9770","COBISSID_HOST:285591811","URN:URN:NBN:SI:doc-9Q5KSCI1"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:source":{"@xml:lang":"sl","#text":"The art of discrete and applied mathematics"},"dc:subject":[{"@xml:lang":"en","#text":"algorithms"},{"@xml:lang":"sl","#text":"algoritmi"},{"@xml:lang":"sl","#text":"devesa"},{"@xml:lang":"en","#text":"hierarchical products of graphs"},{"@xml:lang":"sl","#text":"hierarhični produkti grafov"},{"@xml:lang":"sl","#text":"prafaktorizacije"},{"@xml:lang":"en","#text":"prime factorizations"},{"@xml:lang":"en","#text":"trees"}],"dc:title":{"@xml:lang":"sl","#text":"Hierarchical product graphs and their prime factorization|"},"dc:description":[{"@xml:lang":"sl","#text":"The hierarchical and the generalized hierarchical product of graphs, together with their multiary and rooted versions, are variants of the Cartesian product. They are not commutative, and only the rooted versions are associative. We prove that finite connected graphs have unique prime factorizations with respect to the rooted hierarchical product, the multiary hierarchical product, and the rooted generalized hierarchical product. For the generalized hierarchical product, we disprove a claim about unique prime factorization by Anderson, Guob, Tenney, and Wash from 2017. We also describe the interrelation between the automorphism groups of connected graphs with the groups of their prime factors in the cases of unique prime factorization, and in the case of the standard prime factorization with respect to the hierarchical product. For finite trees, we show that their prime factors can be computed in subquadratic time"},{"@xml:lang":"sl","#text":"Hierarhični in posplošeni hierarhični produkt grafov, skupaj z njunimi večstranskimi in korenskimi različicami, sta različici kartezičnega produkta. Nista komutativna, in samo korenske različice so asociativne. Dokažemo, da imajo končni povezani grafi enolične prafaktorizacije glede na korenski hierarhični produkt, večstranski hierarhični produkt in korenski posplošeni hierarhični produkt. Za posplošeni hierarhični produkt ovržemo trditev Andersona, Gua, Tenneyja in Washa o enolični prafaktorizaciji iz leta 2017. Opišemo tudi medsebojno razmerje med grupami avtomorfizmov povezanih grafov in grupami njihovih prafaktorjev v primerih enolične in standardne prafaktorizacije glede na hierarhični produkt. Za končna drevesa pokažemo, da je njihove prafaktorje mogoče izračunati v subkvadratnem času"}],"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-9Q5KSCI1","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-9Q5KSCI1"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-9Q5KSCI1/129db946-1582-49fd-9eb8-b414148641e5/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-9Q5KSCI1/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-9Q5KSCI1"}}}}