{"?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-XOZJTY61/5c47c202-430e-4824-a839-525851e170fa/PDF","dcterms:extent":"636 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-XOZJTY61/ff878704-28d3-41b1-a7d8-328b727831ed/TEXT","dcterms:extent":"0 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-XOZJTY61","dcterms:issued":"2026","dc:creator":"Popovič, Maša","dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"15 str."},{"@xml:lang":"sl","#text":"številka:2"}],"dc:identifier":["ISSN:2385-8567","COBISSID_HOST:291933955","URN:URN:NBN:SI:doc-XOZJTY61"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Založba Fakultete za matematiko in fiziko Univerze v Ljubljani"},"dc:source":{"@xml:lang":"sl","#text":"Matrika"},"dc:subject":[{"@xml:lang":"en","#text":"cardinality of a set of vertices"},{"@xml:lang":"sl","#text":"celoštevilsko linearno programiranje"},{"@xml:lang":"sl","#text":"cirkulantni grafi"},{"@xml:lang":"en","#text":"clockwise-oriented circulant graphs"},{"@xml:lang":"en","#text":"integer linear programming"},{"@xml:lang":"sl","#text":"kardinalnost množice vozlišč"},{"@xml:lang":"en","#text":"metric dimension of a graph"},{"@xml:lang":"sl","#text":"metrična dimenzija grafa"}],"dc:title":{"@xml:lang":"sl","#text":"Metrične dimenzije usmerjenih cirkulantnih grafov|"},"dc:description":[{"@xml:lang":"sl","#text":"The metric dimension of a graph is the minimum cardinality of a set of vertices that uniquely determines all other vertices of the graph by their distances to the selected vertices. In this paper, the metric dimension of clockwise-oriented circulant graphs ?$C(n, d)$? is studied. First, an integer linear programming formulation for computing the metric dimension of an arbitrary directed graph is presented, and its computational complexity is analyzed. Using computational experiments, the metric dimensions of graphs ?$C(n, d)$? for ?$n \\le 40$? are then determined, and several conjectures and general properties are formulated based on the obtained results. A formula for the distance between arbitrary vertices and an expression for the diameter of the graph ?$C(n, d)$? are derived, and general upper and lower bounds for its metric dimension are established. Furthermore, exact values of the metric dimension are provided for several special families of graphs, including ?$C(n, 1)$?, ?$C(n, 2)$?, ?$C(n, n-1)$?, and ?$C(n, n-2)$?. The results indicate a strong relationship between the parameters ?$n$? and ?$d$? and open several directions for further research on the metric dimension of directed circulant graphs"},{"@xml:lang":"sl","#text":"Metrična dimenzija grafa predstavlja najmanjšo kardinalnost množice vozlišč, s katero se lahko enolično določi vsa ostala vozlišča grafa glede na njihove razdalje do izbranih vozlišč. V članku je obravnavana metrična dimenzija v smeri urinega kazalca usmerjenih cirkulantnih grafov ?$C(n, d)$?. Najprej je predstavljen celoštevilski linearni program za izračun metrične dimenzije poljubnega usmerjenega grafa ter analiza njegove časovne zahtevnosti. Nato so z računalniškimi eksperimenti izračunane metrične dimenzije grafov ?$C(n, d)$? za ?$n \\le 40$? in na podlagi dobljenih rezultatov je oblikovanih več domnev in splošnih lastnosti. Dokazana je formula za razdaljo med poljubnima vozliščema in izraz za premer grafa ?$C(n, d)$? ter izpeljane so splošne zgornje in spodnje meje za metrično dimenzijo. Poleg tega so podane natančne vrednosti metrične dimenzije za nekatere posebne družine grafov, med drugim za ?$C(n, 1)$?, ?$C(n, 2)$?, ?$C(n, n-1)$? in ?$C(n, n-2)$?. Rezultati nakazujejo tesno povezavo med parametroma ?$n$? in ?$d$? ter odpirajo več vprašanj za nadaljnje raziskovanje metrične dimenzije usmerjenih cirkulantnih grafov"}],"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-XOZJTY61","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-XOZJTY61"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-XOZJTY61/5c47c202-430e-4824-a839-525851e170fa/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 v Ljubljani, Fakulteta za matematiko in fiziko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-XOZJTY61/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-XOZJTY61"}}}}