{"?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-EXBJK8SJ/a9c1b184-6854-47fd-a687-796b0c9037ae/PDF","dcterms:extent":"1514 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-EXBJK8SJ/7782d61a-aa8c-4fcd-aecb-b5ad54dfc8b4/TEXT","dcterms:extent":"48 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-EXBJK8SJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Kubota, Sho","Taniguchi, Tetsuji","Yoshino, Kiyoto"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 555-579"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18965593","URN:URN:NBN:SI:doc-EXBJK8SJ"],"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":"Hoffman graph"},{"@xml:lang":"sl","#text":"Hoffmanov graf"},{"@xml:lang":"en","#text":"line graph"},{"@xml:lang":"sl","#text":"najmanjša lastna vrednost"},{"@xml:lang":"sl","#text":"povezavni graf"},{"@xml:lang":"en","#text":"smallest eigenvalue"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On graphs with the smallest eigenvalue at least -1- square root 2, part III|"},"dc:description":[{"@xml:lang":"sl","#text":"There are many results on graphs with the smallest eigenvalue at least ?$-2$?. In order to study graphs with the eigenvalues at least ?$-1 - \\sqrt{2}$?, R. Woo and A. Neumaie Linear Algebra Appl. 226-228, 577-591 (1995) introduced Hoffman graphs and ?$\\mathcal{H}$?-line graphs. They proved that a graph with the sufficiently large minimum degree and the smallest eigenvalue at least ?$-1 - \\sqrt{2}$? is a slim ?$\\{\\mathfrak h_2, \\mathfrak h_5, \\mathfrak h_7, \\mathfrak h_9\\}$?-line graph. After that, the second author Ars Math. Contemp. 5, No. 2, 243--258 (2012) researched on slim ?$\\{\\mathfrak h_2, \\mathfrak h_5\\}$?-line graphs. As an analogue, we reveal the condition under which a strict ?$\\{\\mathfrak h_1, \\mathfrak h_4, \\mathfrak h_7\\}$?-cover of a slim ?$\\{\\mathfrak h_7\\}$?-line graph is unique, and completely determine the minimal forbidden graphs for the slim ?$\\{\\mathfrak h_7\\}$?-line graphs"},{"@xml:lang":"sl","#text":"Obstajajo številni rezultati o grafih, katerih najmanjša lastna vrednost je vsaj ?$-2$?. Kot orodje za raziskavo grafov, katerih lastne vrednosti so vsaj ?$-1 - \\sqrt{2}$?, sta R. Woo in A. Neumaier vpeljala Hoffmanove grafe in ?$\\mathcal{H}$?-povezavne grafe. Dokazala sta, da je graf, ki ima dovolj veliko najmanjšo stopnjo in katerega najmanjša lastna vrednost je vsaj ?$-1 - \\sqrt{2}$?, tanek ?$\\{\\mathfrak h_2, \\mathfrak h_5, \\mathfrak h_7, \\mathfrak h_9\\}$?-povezavni graf. Po tem je T. Taniguchi raziskoval tanke ?$\\{\\mathfrak h_2, \\mathfrak h_5\\}$?-povezavne grafe. Po analogiji v tem članku razkrivamo pogoje, pod katerimi je strogi ?$\\{\\mathfrak h_1, \\mathfrak h_4, \\mathfrak h_7\\}$-krov tankega $\\{\\mathfrak h_7\\}$?-povezavnega grafa en sam, in popolnoma določimo minimalne prepovedane grafe za tanke $?\\{\\mathfrak h_7\\}$?-povezavne grafe"}],"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-EXBJK8SJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-EXBJK8SJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-EXBJK8SJ/a9c1b184-6854-47fd-a687-796b0c9037ae/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-EXBJK8SJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-EXBJK8SJ"}}}}