{"?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-WJWRZ24P/8bb40c65-d79d-4a25-9fa2-95df0436ead6/PDF","dcterms:extent":"379 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-WJWRZ24P/60e1f2a9-ebf4-4945-8a2c-f9049b61474f/TEXT","dcterms:extent":"59 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-WJWRZ24P","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["MacLean, Mark","Miklavič, Štefko"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 187-210"}],"dc:identifier":["ISSN:1855-3966","COBISSID:22957059","URN:URN:NBN:SI:doc-WJWRZ24P"],"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":"teorija grafov"},{"@xml:lang":"sl","#text":"Terwilligerjeva algebra"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On a certain class of 1-thin distance-regular graphs|"},"dc:description":{"@xml:lang":"sl","#text":"Naj bo ?$\\Gamma$? ne-dvodelen razdaljno-regularen graf z množico vozlišč ?$X$?, premerom ?$D \\ge 3$?, ter stopnjo ?$k \\ge 3$?. Izberimo si vozlišče ?$x \\in X$? in naj bo ?$T=T(x)$? Terwilligerjeva algebra grafa ?$\\Gamma$? glede na ?$x$?. Za vsako vozlišče ?$z \\in X$? in za ?$0 \\le i \\le D$? naj bo ?$\\Gamma_i(z)=\\{w \\in X : \\partial(z, w) = i\\}$? označimo ?$D_j^i = D_j^i(x, y) = \\Gamma_i(x) \\cap \\Gamma_j(y)$? in za dano vozlišče ?$y$? definirajmo preslikavi ?$H_i \\colon D_i^i \\to \\mathbb{Z}$? in ?$V_i \\colon D_{i-1}^i \\to \\mathbb{Z}$? takole: ?$$H_i(z) = |\\Gamma_1(z) \\cap D_{i-1}^{i-1}|, \\quad V_i(z) = |\\Gamma_1(z) \\cap D_{i-1}^{i-1}|.$$? Privzemimo, da sta za vsako vozlišče ?$y \\in \\Gamma_1(x)$? in za vsak ?$2 \\le i \\le D$? pripadajoči preslikavi ?$H_i$? in ?$V_i$? konstantni, ter da te konstante niso odvisne od izbire vozlišča ?$y$?. Dalje tudi privzemimo, da so konstantne vrednosti preslikav ?$H_i$? neničelne za ?$2 \\le i \\le D$?. Pokažemo, da je vsak nerazcepen ?$T$?-modul s krajiščem 1 tanek. Nadalje tudi pokažemo, da ima ?$\\Gamma$? do izomorfizma natančno natanko tri nerazcepne ?$T$?-module s krajiščem 1 natanko takrat, ko veljajo trije kombinatorični pogoji (ki jih definiramo kasneje). Kot primer pokažemo, da ti trije kombinatorični pogoji veljajo za Johnsonove grafe ?$J(n, m)$?, kjer je ?$n \\ge 7$?, ?$3 \\le m < n/2$?"},"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-WJWRZ24P","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-WJWRZ24P"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-WJWRZ24P/8bb40c65-d79d-4a25-9fa2-95df0436ead6/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-WJWRZ24P/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-WJWRZ24P"}}}}