{"?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-0COBRRGY/ed4583f3-8d7d-4a41-91df-d41c25683837/PDF","dcterms:extent":"341 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0COBRRGY/e32a5acb-2464-48aa-a593-94194471c484/TEXT","dcterms:extent":"42 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-0COBRRGY","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Brešar, Boštjan","Hartnell, Bert L.","Rall, Douglas F."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 293-306"}],"dc:identifier":["COBISSID:18064729","ISSN:1855-3966","URN:URN:NBN:SI:doc-0COBRRGY"],"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":"disociacijsko število"},{"@xml:lang":"sl","#text":"dobro pokriti grafi"},{"@xml:lang":"sl","#text":"Moore-ovi grafi"},{"@xml:lang":"sl","#text":"ožina"},{"@xml:lang":"sl","#text":"polarnostni grafi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Uniformly dissociated graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A set ?$D$? of vertices in a graph ?$G$? is called a dissociation set if every vertex in ?$D$? has at most one neighbor in ?$D$?. We call a graph ?$G$? uniformly dissociated if all maximal dissociation sets are of the same cardinality. Characterizations of uniformly dissociated graphs with small cardinalities of dissociation sets are proven; in particular, the graphs in which all maximal dissociation sets are of cardinality 2 are the complete graphs on at least two vertices from which possibly a matching is removed, while the graphs in which all maximal dissociation sets are of cardinality 3 are the complements of the ?$K_4$?-free geodetic graphs with diameter 2. A general construction by which any graph can be embedded as an induced subgraph of a uniformly dissociated graph is also presented. In the main result we characterize uniformly dissociated graphs with girth at least 7 to be either isomorphic to ?$C_7$?, or obtainable from an arbitrary graph ?$H$? with girth at least 7 by identifying each vertex of ?$H$? with a leaf of a copy of ?$P_3$?"},{"@xml:lang":"sl","#text":"Množica vozlišč ?$D$? grafa ?$G$? se imenuje disociacijska množica, če ima vsako vozlišče množice ?$D$? največ enega soseda iz ?$D?$. Pravimo, da je graf enakomerno disociiran, če imajo vse njegove maksimalne disociacijske množice isto moč. V članku dokažemo karakterizacije enakomerno disociiranih grafov z majhnimi močmi disociacijskih množic; tako so grafi, v katerih imajo vse maksimalne disociacijske množice dva elementa, natanko polni grafi na vsaj dveh vozliščih, iz katerih so lahko odstranjene tudi povezave kakega prirejanja, medtem ko so grafi, v katerih so vse maksimalne disociacijske množice moči 3, natanko komplementi geodetskih grafov z diametrom 2, ki nimajo induciranih podgrafov izomorfnik ?$K_4$?. Predstavimo tudi splošno konstrukcijo, s katero lahko poljuben graf vložimo kot induciran podgraf v nek enakomerno disociiran graf. Glavni rezultat je karakterizacija enakomerno disociiranih grafov, v katerih so vsi cikli dolžine vsaj 7, kot grafov, ki so bodisi izomorfni grafu ?$C_7$? ali pa jih lahko dobimo iz poljubnega grafa ?$H$?, v katerem so vsi cikli dolžine vsaj 7, tako da identificiramo vsako vozlišče grafa ?$H$? z listom kopije grafa ?$P_3$?"}],"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-0COBRRGY","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0COBRRGY"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0COBRRGY/ed4583f3-8d7d-4a41-91df-d41c25683837/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-0COBRRGY/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0COBRRGY"}}}}