{"?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-3TUCUIG9/6eee73fb-99fe-4a15-8cea-cad88505b27b/PDF","dcterms:extent":"402 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3TUCUIG9/cfef14b4-f5d7-4efb-aff3-9b173c55ad73/TEXT","dcterms:extent":"42 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3TUCUIG9/c9649cd2-0f1c-4351-9358-7be2689118bd/PDF","dcterms:extent":"141 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3TUCUIG9/0c91333d-5419-446b-8704-b510239bb8c7/TEXT","dcterms:extent":"3 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-3TUCUIG9","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":"Shi, Lingjuan","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P1.05 (16 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2631.be0","COBISSID_HOST:143830019","ISSN:1855-3966","URN:URN:NBN:SI:doc-3TUCUIG9"],"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":"efficient dominating set"},{"@xml:lang":"sl","#text":"fulerenski graf"},{"@xml:lang":"en","#text":"fullerene graph"},{"@xml:lang":"en","#text":"perfect star packing"},{"@xml:lang":"sl","#text":"popolno zvezdno pakiranje"},{"@xml:lang":"sl","#text":"učinkovita dominantna množica"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The fullerene graphs with a perfect star packing|"},"dc:description":[{"@xml:lang":"sl","#text":"Fullerene graph ?$G$? is a connected plane cubic graph with only pentagonal and hexagonal faces, which is the molecular graph of carbon fullerene. A spanning subgraph of ?$G$? is called a perfect star packing in ?$G$? if its each component is isomorphic to ?$K_{1,3}$?. For an independent set ?$D \\subseteq V(G)$?, if each vertex in ?$V(G) \\setminus D$? has exactly one neighbor in ?$D$?, then ?$D$? is called an efficient dominating set of ?$G$?. In this paper we show that the number of vertices of a fullerene graph admitting a perfect star packing must be divisible by 8. This answers an open problem asked by Došlić et al. and also shows that a fullerene graph with an efficient dominating set has $8n$ vertices. In addition, we find some counterexamples for the necessity of Theorem 14 of paper of T. Došlić et al. J. Math. Chem. 58, No. 10, 2223-2244 (2020) and list some subgraphs that preclude the existence of a perfect star packing of type ?$P0$?"},{"@xml:lang":"sl","#text":"Fulerenski graf ?$G$? je povezan ravninski kubični graf s samimi peterokotnimi in šesterokotnimi lici, ki predstavlja molekularni graf ogljikovega fulerena. Vpeti podgraf grafa ?$G$? se imenuje popolno zvezdno pakiranje v grafu ?$G$?, če je vsaka njegova komponenta izomorfna ?$K_{1,3}$?. Neodvisna množica ?$D \\subseteq V(G)$?, v kateri ima vsako vozlišče iz ?$V(G) \\setminus D$? natanko enega soseda v ?$D$?, se imenuje učinkovita dominantna množica grafa ?$G$?. V tem pokažemo, da mora biti število vozlišč fulerenskega grafa, ki dopušča popolno zvezdno pakiranje, deljivo z 8. To odgovarja na odprt problem, ki so ga zastavili Došlić in dr. in kaže, da ima fulerenski graf z učinkovito dominantno množico ?$8n$? vozlišč. Pokažemo tudi nekaj protiprimerov za nujnost izreka 14 v članku Došlić in dr. J. Math. Chem. 58, No. 10, 2223-2244 (2020) in prikažemo nekatere podgrafe, ki izključujejo obstoj popolnega zvezdnega pakiranja tipa ?$P0$?"}],"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-3TUCUIG9","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-3TUCUIG9"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-3TUCUIG9/6eee73fb-99fe-4a15-8cea-cad88505b27b/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-3TUCUIG9/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-3TUCUIG9"}}}}