{"?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-MKQNV7AD/77748fc8-e701-4ff7-a171-183b511de6d4/PDF","dcterms:extent":"428 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-MKQNV7AD/202143cc-cf7d-4f85-ab41-52f5d8770f81/TEXT","dcterms:extent":"32 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-MKQNV7AD","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Deng, Shibing","Li, Shuchao","Song, Feifei"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:11"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 285-299"}],"dc:identifier":["COBISSID:17856857","ISSN:1855-3966","URN:URN:NBN:SI:doc-MKQNV7AD"],"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":"adjacency matrix"},{"@xml:lang":"en","#text":"inertia"},{"@xml:lang":"sl","#text":"sosednostna matrika"},{"@xml:lang":"sl","#text":"utežen k-cikličen graf"},{"@xml:lang":"sl","#text":"vztrajnost"},{"@xml:lang":"en","#text":"weighted k-cyclic graph"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the inertia of weighted (k - 1)-cyclic graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G_w$? be a weighted graph. The inertia of ?$G_w$? is the triple ?$\\mathrm{In} (G_w)=(i_+ (G_w), i_ - (G_w), i_0(G_w))$?, where ?$i _+ (G_w)$?, ?$i_- (G_w)$?, ?$i_0(G_w)$? are, respectively, the number of the positive, negative and zero eigenvalues of the adjacency matrix ?$A(G_w)$? of ?$G_w$? including their multiplicities. A simple ?$n$?-vertex connected graph is called a ?$(k - 1)$?-cyclic graph provided that its number of edges equals ?$n + k - 2$?. Let ?$\\theta(r_1, r_2, \\dots, r_k)_w$? be an ?$n$?-vertex simple weighted graph obtained from ?$k$? weighted paths ?$(P_{r_1})_w, ((P_{r_2})_w, \\dots,(P_{r_k})_w$? by identifying their initial vertices and terminal vertices, respectively. Set ?$\\Theta_ k: = \\{\\theta(r_1, r_2, \\dots, r_k)_w \\colon r_1 + r_2 + \\dots + r_k = n + 2k - 2\\}$?. The inertia of the weighted graph ?$\\theta(r_1, r_2, \\dots, r_k)_w$? is studied. Also, the weighted ?$(k - 1)$?-cyclic graphs that contain ?$\\theta(r_1, r_2, \\dots, r_k)_w$? as an induced subgraph are studied. We characterize those graphs among ?$\\Theta_ k$? that have extreme inertia. The results generalize the corresponding results obtained in X.Z. Tan, B.L. Liu, The nullity of (k - 1)-cyclic graphs, Linear Algebra Appl. 438 (2013) 3144-3153 and G.H. Yu et al., The inertia of weighted unicyclic graphs, Linear Algebra Appl. 448 (2014) 130-152"},{"@xml:lang":"sl","#text":"Naj bo ?$G_w$? utežen graf. Vztrajnost grafa ?$G_w$? je urejena trojica ?$\\mathrm{In} (G_w) = (i_+ (G_w), i_ - (G_w), i_0(G_w))$?, kjer so ?$i _+ (G_w)$?, ?$i_- (G_w)$?, ?$i_0(G_w)$? število pozitivnih, negativnih in ničelnih lastnih vrednosti sosednostne matrike ?$A(G_w)$? grafa ?$G_w$? upoštevaje njihove večkratnosti. Enostaven ?$n$?-vozliščni povezan graf se imenuje ?$(k -1)$?-cikličen graf, če je število njegovih povezav enako ?$n+k-2$?. Naj bo ?$\\theta(r_1, r_2, \\dots, r_k)_w$? ?$n$?-vozliščni enostaven utežen graf, ki ga dobimo iz ?$k$? uteženih poti ?$(P_{r_1})_w, ((P_{r_2})_w, \\dots,(P_{r_k})_w$? z identificiranjem njihovih začetnih vozlišč ter njihovih končnih vozlišč. Vpeljimo ?$\\Theta_ k: = \\{\\theta(r_1, r_2, \\dots, r_k)_w \\colon r_1 + r_2 + \\dots + r_k = n + 2k - 2\\}$?. Študiramo vztrajnost uteženega grafa ?$\\theta(r_1, r_2, \\dots, r_k)_w$?. Prav tako študiramo utežene ?$(k - 1)$?-ciklične grafe, ki vsebujejo ?$\\theta(r_1, r_2, \\dots, r_k)_w$? kot induciran podgraf. Karakteriziramo tiste grafe izmed ?$\\Theta_ k$?, ki imajo ekstremno vztrajnost. Naši rezultati posplošujejo tiste, ki sta jih dobila Tan in Liu leta 2013 ter Yu in dr. leta 2014"}],"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-MKQNV7AD","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-MKQNV7AD"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-MKQNV7AD/77748fc8-e701-4ff7-a171-183b511de6d4/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-MKQNV7AD/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-MKQNV7AD"}}}}