{"?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-14CDJEL0/de2f1f3c-57ac-48ad-8b33-d1cff695a241/PDF","dcterms:extent":"457 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-14CDJEL0/8cabfdf5-59de-4cae-8b4d-f384c51a85af/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-14CDJEL0","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Hammack, Richard H.","Smith, Gregory D."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:12"},{"@xml:lang":"sl","#text":"str. 183-203"}],"dc:identifier":["COBISSID:18099289","ISSN:1855-3966","URN:URN:NBN:SI:doc-14CDJEL0"],"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":"grafi"},{"@xml:lang":"sl","#text":"markovske verige"},{"@xml:lang":"sl","#text":"produkti grafov"},{"@xml:lang":"sl","#text":"prostori ciklov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Cycle bases of reduced powers of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We define what appears to be a new construction. Given a graph ?$G$? and a positive integer ?$k$?, the reduced ?$k$?th power of ?$G$?, denoted ?$G^{(k)}$?, is the configuration space in which ?$k$? indistinguishable tokens are placed on the vertices of ?$G$?, so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide a construction of minimum cycle bases of ?$G^{(k)}$?. The minimum cycle basis construction is an interesting combinatorial problem that is also useful in applications involving configuration spaces. For example, if ?$G$? is the state-transition graph of a Markov chain model of a stochastic automaton, the reduced power ?$G^{(k)}$? is the state-transition graph for ?$k$? identical (but not necessarily independent) automata. We show how the minimum cycle basis construction of ?$G^{(k)}$? may be used to confirm that state-dependent coupling of automata does not violate the principle of microscopic reversibility, as required in physical and chemical applications"},{"@xml:lang":"sl","#text":"Definiramo konstrukcijo, za katero menimo, da je nova. Če je dan graf ?$G$? in pozitivno celo število ?$k$?, potem je reducirana ?$k$?-ta potenca grafa ?$G$?, ki jo označimo ?$G^{(k)}$?, konfiguracijski prostor, v katerem postavimo ?$k$? enakih žetonov na vozlišča grafa ?$G$?, tako da je na vsakem vozlišču največ ?$k$? žetonov. Dve konfiguraciji sta sosedni, če lahko eno transformiramo v drugo tako, da premaknemo en žeton vzdolž povezave v neko sosedno vozlišče. Predstavimo trditve, ki se nanašajo na strukturne lastnosti reduciranih potenc grafa in, kar je najbolj pomembno, zagotavljajo konstrukcijo minimalne baze ciklov potenc ?$G^{(k)}$?. Konstruiranje minimalne baze ciklov je zanimiv kombinatoričen problem, ki je koristen tudi v uporabah, ki vključujejo konfiguracijske prostore. Na primer, če je ?$G$? graf prehodnih stanj modela markovskih verig stohastičnega avtomata, potem je reducirana potenca ?$G^{(k)}$? graf prehodnih stanj za ?$k$? identičnih (a ne nujno neodvisnih) avtomatov. Pokažemo, kako se da konstrukcijo minimalne baze ciklov grafa of ?$G^{(k)}$? uporabiti za dokaz, da od stanj odvisno parjenje avtomatov ne krši načela mikroskopske reverzibilnosti, kot se zahteva pri fizikalnih in kemičnih aplikacijah"}],"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-14CDJEL0","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-14CDJEL0"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-14CDJEL0/de2f1f3c-57ac-48ad-8b33-d1cff695a241/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-14CDJEL0/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-14CDJEL0"}}}}