{"?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-H48D12J0/26978e8b-22c6-46d5-816c-50b6e29326e0/PDF","dcterms:extent":"370 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-H48D12J0/d43fbbb1-6b7d-4733-b4a3-2dec8355f783/TEXT","dcterms:extent":"25 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-H48D12J0/4ef52914-00ec-4062-a950-a30ab93a44f8/PDF","dcterms:extent":"207 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-H48D12J0/5885b9b3-0541-49dc-b693-3cfdea0e5b9d/TEXT","dcterms:extent":"3 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-H48D12J0","dcterms:issued":"2025","dc:creator":["Smith, Jason P.","Zahedi, Emad"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.05"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 1-10"}],"dc:identifier":["DOI:10.26493/2590-9770.1813.5ce","ISSN:2590-9770","COBISSID_HOST:285852163","URN:URN:NBN:SI:doc-H48D12J0"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:source":{"@xml:lang":"sl","#text":"The art of discrete and applied mathematics"},"dc:subject":[{"@xml:lang":"en","#text":"chordal"},{"@xml:lang":"en","#text":"cut vertex"},{"@xml:lang":"en","#text":"distance preserving"},{"@xml:lang":"en","#text":"isometric subgraph"},{"@xml:lang":"sl","#text":"izometrični podgraf"},{"@xml:lang":"sl","#text":"izrezana točka"},{"@xml:lang":"sl","#text":"ohranjanje razdalje"},{"@xml:lang":"en","#text":"sequentially distance preserving"},{"@xml:lang":"en","#text":"simplicial vertex"},{"@xml:lang":"sl","#text":"simplicialna točka"},{"@xml:lang":"sl","#text":"tetiva"},{"@xml:lang":"sl","#text":"zaporedno ohranjanje razdalje"}],"dc:title":{"@xml:lang":"sl","#text":"On distance preserving and sequentially distance preserving graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A graph H is an isometric subgraph of G if d_H(u,v)=d_G(u,v), for every pair u,v ? V(H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i?1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles"},{"@xml:lang":"sl","#text":"Graf H je izometričen podgraf grafa G, če je dH(u, v) =dG(u, v), za vsak par točk u, v?V(H). Graf ohranja razdaljo, če ima izometričen podgraf vsakega možnega reda. Graf zaporedno ohranja razdaljo, če se da njegove točke urediti tako, da z izbrisom prvih i točk dobimo izometričen podgraf, kar mora veljati za vse i?1. Podamo ekvivalenten pogoj za zaporedno ohranjanje razdalj, osnovan na simplicialnih ureditvah. Z uporabo tega pogoja dokažemo: če graf ne vsebuje nobenih induciranih ciklov dolžine 5 ali večjih, potem zaporedno ohranja razdalje in posledično ohranja razdalje. Obravnavamo tudi lastnost ohranjanja razdalj na grafih z rezno točko. Definiramo še družino grafov, ki ne ohranjajo razdalje, konstruirani pa so iz ciklov"}],"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-H48D12J0","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-H48D12J0"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-H48D12J0/26978e8b-22c6-46d5-816c-50b6e29326e0/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-H48D12J0/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-H48D12J0"}}}}