{"?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-0EALPE8Q/ba62-ac-b-2610c8f5614eee1c19405-b96c/PDF","dcterms:extent":"965 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-0EALPE8Q/78f7c192-1af2-4830-9bf3-9cd04af0a5cc/TEXT","dcterms:extent":"173 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-0EALPE8Q/e4e131cf-2b43-459d-960d-40609b92941e/WEB","dcterms:extent":"0 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-0EALPE8Q","dcterms:issued":"2022","dc:contributor":"Klavžar, Sandi","dc:creator":"Rus, Gregor","dc:format":{"@xml:lang":"sl","#text":"XI f., 128 str., 31 cm"},"dc:identifier":["COBISSID:124417283","URN:URN:NBN:SI:doc-0EALPE8Q"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"G. Rus"},"dc:source":{"@xml:lang":"sl","#text":"visokošolska dela"},"dc:subject":[{"@xml:lang":"sl","#text":"Cikli"},{"@xml:lang":"en","#text":"cycles"},{"@xml:lang":"sl","#text":"Disertacije"},{"@xml:lang":"en","#text":"distance-balanced graphs"},{"@xml:lang":"en","#text":"doctoral theses"},{"@xml:lang":"sl","#text":"doktorske disertacije"},{"@xml:lang":"en","#text":"general position set"},{"@xml:lang":"en","#text":"gp-number"},{"@xml:lang":"sl","#text":"gp-število"},{"@xml:lang":"sl","#text":"Grafi"},{"@xml:lang":"sl","#text":"grafovski produkti"},{"@xml:lang":"en","#text":"graph products"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"en","#text":"l-distance-balanced graphs"},{"@xml:lang":"sl","#text":"l-razdaljno-uravnoteženi grafi"},{"@xml:lang":"sl","#text":"množica vozlišč v splošni legi"},{"@xml:lang":"en","#text":"paths"},{"@xml:lang":"sl","#text":"poti"},{"@xml:lang":"sl","#text":"razdaljno-uravnoteženi grafi"},{"@xml:lang":"sl","#text":"Teorija grafov"},{"@xml:lang":"sl","#text":"Univerzitetna in visokošolska dela"}],"dc:title":{"@xml:lang":"sl","#text":"Nekaj metričnih lastnosti grafovskih produktov| doktorska disertacija|"},"dc:description":[{"@xml:lang":"sl","#text":"The dissertation focuses on two concepts: the general position problem and the l-distance-balancness property in graphs. The general position problem was introduced lately in paper by Manuel and Klavžar from 2018, while l-distance-balanced graphs were first studied in Frelih's doctoral thessis in 2014. In the disseration we present new results, which are mainly connected to different graph products. We determine the exact value of the gp-number in the Cartesian product of arbitrary number of path graphs, precisely that ?$\\gp(P^{\\cp,n}) = 2^{2^{n-1}}$? hold. We also determine the exact value of the gp-number in the Cartesian product of a path and a cycle and in the Cartesian product of two cycle graphs. Also the gp-value in some Kneser graphs is presented. In the second part we prove when the lexicographic product of ?$GH$? is an ?$\\ell$?-distance-balanced graph, for any ?$\\ell \\in \\{3,\\ldots,\\diam(G)\\}$?. A similar condition is derived to test whether the corona product is ?$\\ell$?-distance-balanced. We also study and characterize when the Cartesian product ?$G\\cp K_n$? is l-distance-balanced"},{"@xml:lang":"sl","#text":"Doktorska disertacija obravnava koncepta množice vozlišč v splošni legi v grafih in l-razdaljno-uravnoteženost grafov. Oba koncepta sta bila v tej obliki vpeljana nedavno, splošna lega leta 2018 v članku avtorjev Manuela in Klavžarja, l-razdaljna uravnoteženost pa v doktorski disertaciji Freliha leta 2014. V disertaciji so predstavljeni novi rezultati, ki so večinoma povezani z različnimi grafovskimi produkti. Dokazana je točna vrednost gp-števila v kartezičnem produktu poljubnega števila poti, natančneje, da velja ?$\\gp(P^{\\cp,n}) = 2^{2^{n-1}}$?. Dokazana je točna vrednost gp-števila v produktu poti in cikla in produkta dveh ciklov. Dokazana je tudi točna vrednost gp-števila v nekaterih Kneserjevih grafih. V razdelku, ki se ukvarja z l-razdaljno-uravnoteženostjo, je pokazan pogoj, kdaj je leksikografski produkt grafov ?$GH$? ?$\\ell$?-razdaljno-uravnotežen za poljuben ?$\\ell \\in \\{3,\\ldots,\\diam(G)\\}$?. Prav tako je dokazano, kdaj je ?$\\ell$?-razdaljno-uravnotežen korona produkt. Določimo pa tudi pogoj, kdaj je ?$\\ell$?-razdaljno uravnotežen kartezični produkt ?$G\\cp K_n.$?"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"visokošolska dela"},{"@xml:lang":"en","#text":"theses and dissertations"},{"@rdf:resource":"http://www.wikidata.org/entity/Q1266946"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-0EALPE8Q","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-0EALPE8Q"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-0EALPE8Q/ba62-ac-b-2610c8f5614eee1c19405-b96c/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"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 v Mariboru, Fakulteta za naravoslovje in matematiko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-0EALPE8Q/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-0EALPE8Q"}}}}