{"?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-0ZJWJUJU/a3e26e98-8868-4ea9-be69-80ce88fc52da/PDF","dcterms:extent":"274 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0ZJWJUJU/1fd30a8b-4d3e-4b19-a988-1255041b2362/TEXT","dcterms:extent":"14 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-0ZJWJUJU","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2014","dc:creator":"Anholcer, Marcin","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 23-29"}],"dc:identifier":["COBISSID:16792153","ISSN:1855-3966","URN:URN:NBN:SI:doc-0ZJWJUJU"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"en","#text":"product irregularity strength"},{"@xml:lang":"en","#text":"product-irregular labeling"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@xml:lang":"en","#text":"tree"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Product irregularity strength of certain graphs|"},"dc:description":{"@xml:lang":"sl","#text":"Consider a simple graph ?$G$? with no isolated edges and at most one isolated vertex. A labeling ?$w \\colon E(G) \\to \\{1, 2, \\dots,m\\}$? is called product - irregular, if all product degrees ?$pdG(v) = \\prod_{e \\ni v}w(e)$? are distinct. The goal is to obtain a product - irregular labeling that minimizes the maximal label. This minimal value is called the product irregularity strength and denoted ?$ps(G)$?. We give the exact values of ?$ps(G)$? for several families of graphs, as complete bipartite graphs ?$K_{m, n}$?, where ?$2 \\le m \\le n \\le {m + 2 \\choose 2}$?, some families of forests, including complete ?$d$?-ary trees, and other graphs with ?$\\delta(G) = 1$?"},"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-0ZJWJUJU","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0ZJWJUJU"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0ZJWJUJU/a3e26e98-8868-4ea9-be69-80ce88fc52da/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-0ZJWJUJU/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0ZJWJUJU"}}}}