{"?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-OO3KONYL/73aa2701-fb23-46d6-ba83-9401dd28a4f3/PDF","dcterms:extent":"485 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-OO3KONYL/f8f5268b-06f2-4580-bd0c-3901c230e9c7/TEXT","dcterms:extent":"65 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-OO3KONYL","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Cabrera Martinez, Abel","Estrada-Moreno, Alejandro","Rodríguez-Velázquez, Juan Alberto"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P1.04 (25 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2318.fb9","COBISSID_HOST:115274243","ISSN:1855-3966","URN:URN:NBN:SI:doc-OO3KONYL"],"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":"Italian domination"},{"@xml:lang":"sl","#text":"italijanska dominacija"},{"@xml:lang":"sl","#text":"k-dominacija"},{"@xml:lang":"en","#text":"k-domination"},{"@xml:lang":"sl","#text":"k-kratna dominacija"},{"@xml:lang":"en","#text":"k-tuple domination"},{"@xml:lang":"sl","#text":"leksikografski produkt grafov"},{"@xml:lang":"en","#text":"lexicographic product graph"},{"@xml:lang":"sl","#text":"w-dominacija"},{"@xml:lang":"en","#text":"w-domination"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"From Italian domination in lexicographic product graphs to w-domination in graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"R. Ehrenborg Ann. Comb. 18, No. 1, 75-81 (2014) noted that all tilings of a bipartite planar graph are encoded by its cubical matching complex and claimed that this complex is collapsible. We point out to an oversight in his proof and explain why these complexes can be the disjoint union of two or more collapsible complexes. We also prove that all links in these complexes are suspensions up to homotopy. Furthermore, we extend the definition of a cubical matching complex to planar graphs that are not necessarily bipartite, and show that these complexes are either contractible or a disjoint union of contractible complexes. For a simple connected region that can be tiled with dominoes ?$(2 \\times 1$? and ?$1 \\times 2)$? and ?$2 \\times 2$? squares, let ?$f_i$? denote the number of tilings with exactly ?$i$? squares. We prove that ?$f_0 - f_1 + f_2 - f_3 + \\cdots = 1$? (established by Ehrenborg loc. cit.) is the only linear relation for the numbers ?$f_i$?"},{"@xml:lang":"sl","#text":"V članku pokažemo, da je mogoče indeks italijanske dominacije vsakega leksikografskega produkta grafov ?$G \\circ H$? izraziti s pomočjo petih različnih dominacijskih parametrov grafa ?$G$?. Te parametre se da definirati z naslednjim poenotenim pristopom, ki zajema definicijo več dobro znanih dominacijskih parametrov, vpelje pa tudi nove. Naj ?$N(v)$? označuje odprto okolico vozlišča ?$v \\in V(G)$? in naj bo ?$w = (w_0, w_1, \\dots, w_l)$? vektor nenegativnih celih števil, pri čemer je ?$w_0 \\geq 1$?. Pravimo, da je funkcija ?$f: V(G) \\rightarrow \\{0, 1, \\dots, l\\}$? ?$w$?- ominirajoča, če je ?$f(N(v)) = f(N(v)) = \\sum_{u \\in N(v)}f(u) \\geq w_i$? za vsako vozlišče ?$v$?, za katero je ?$f(v) = i$.? Teža funkcije ?$f$? je definirana kot ?$\\omega (f) = \\sum_{v \\in V(G)}f(v)$?, ?$w$?-dominacijski indeks grafa ?$G$?, označen z ?$\\gamma_w(G)$?, pa je minimalna teža vseh ?$w$?-dominacijskih funkcij na grafu ?$G$?. Pokažemo, da je ?$\\gamma_I(G \\circ H) = \\gamma_w(G)$?, kjer je ?$w\\in{2} \\times \\{0, 1, 2\\}^l$? in ?$l\\in \\{2, 3\\}$?. Če takšna enakost velja za specifične vrednosti ?$w_0, \\dots, w_l$?, je odvisno od vrednosti dominacijskega indeksa grafa ?$H$?. Ta članek prinaša preliminarne rezultate v zvezi z ?$\\gamma_w(G)$? in zastavlja izziv za podroben študij te teme"}],"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-OO3KONYL","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-OO3KONYL"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-OO3KONYL/73aa2701-fb23-46d6-ba83-9401dd28a4f3/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-OO3KONYL/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-OO3KONYL"}}}}