{"?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-Q7LD3P0R/5adf2e29-be93-4b3b-8d44-0b1f6625f86d/PDF","dcterms:extent":"420 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q7LD3P0R/13e9c001-cbf9-41e0-b460-45ee72026616/TEXT","dcterms:extent":"43 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q7LD3P0R/cdf54478-21ca-499a-9871-86b8d2c9a32a/PDF","dcterms:extent":"131 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q7LD3P0R/80face9f-deaa-4069-8bac-cc645a477af9/TEXT","dcterms:extent":"3 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-Q7LD3P0R","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Benítez-Bobadilla, Germán","Pastrana-Ramírez, Laura"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1, article  p1.02"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-16"}],"dc:identifier":["DOI:10.26493/1855-3974.2988.2bf","ISSN:1855-3974","COBISSID_HOST:288313859","URN:URN:NBN:SI:doc-Q7LD3P0R"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"en","#text":"cartesian product"},{"@xml:lang":"en","#text":"in-domatic number"},{"@xml:lang":"en","#text":"in-domatically critical digraph"},{"@xml:lang":"en","#text":"in-domatically full digraph"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"en","#text":"line digraph"},{"@xml:lang":"sl","#text":"povezavni digraf"},{"@xml:lang":"sl","#text":"vhodno dominacijski polni digraf"},{"@xml:lang":"sl","#text":"vhodno dominacijsko kritičen digraf"},{"@xml:lang":"sl","#text":"vhodno dominacijsko število"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"In-domatic number and some operations in digraphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Let D be a digraph, a subset S of V(D) is called in-dominating set in D if for each vertex x ? V(D) \\ S there is a vertex w ? S such that (x, w) ? A(D). An in-domatic partition of D is a partition of V(D) where all parts are in-dominating sets in D. The maximum number of parts of an in-domatic partition of D is the in-domatic number of D and it is denoted by d?(D). In this work, the in-domatic number for some families of digraphs such as complete digraphs, transitive digraphs, directed cycles and the cartesian product of two cycles, is calculated. Also, in-domatically critical digraphs are characterized. Additionally, the in-domatic partitions of the line digraph and some other operations which reflect the adjacency and incidence relations in digraphs are explored"},{"@xml:lang":"sl","#text":"Naj bo D usmerjen graf. Podmnožica S množice V (D) se imenuje vhodno dominacijska množica v D, če za vsako vozlišče x ? V (D) \\ S obstaja tako vozlišče w ? S, da je (x, w) ? A(D). Vhodno dominacijska particija grafa D je taka razdelitev množice V (D), da so vsi deli vhodno dominacijske množice v D. Največje število delov v vhodno dominacijski particiji grafa D imenujemo vhodno dominacijsko število grafa D in ga označimo z d-(D). V tem delu izračunamo vhodno dominacijsko število za nekatere družine usmerjenih grafov, kot so popolni usmerjeni grafi, tranzitivni grafi, usmerjeni cikli in kartezični produkt dveh ciklov. Prav tako opišemo vhodno dominacijsko kritične usmerjene grafe. Dodatno raziskujemo vhodno dominacijske particije digrafa povezav in nekatere druge operacije, ki odražajo sosednostne in incidenčne relacije v usmerjenih grafih"}],"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-Q7LD3P0R","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-Q7LD3P0R"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q7LD3P0R/5adf2e29-be93-4b3b-8d44-0b1f6625f86d/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-Q7LD3P0R/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-Q7LD3P0R"}}}}