0 KB244 KB35 KB200820252009Sciriha, Ireneštevilka:2letnik:2str. 217-229COBISSID:15498841ISSN:1855-3966URN:URN:NBN:SI:doc-YJPF5NNGenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneamatematikamatrika sosednostisingularne konfiguracijeteorija grafovMaximal core size in singular graphs|A graph ?$G$? is singular of nullity ?$\eta$? if the nullspace of its adjacency matrix ?${\boldsymbol G}$? has dimension ?$\eta$?. Such a graph contains ?$\eta$? cores determined by a basis for the nullspace of ?${\boldsymbol G}$?. These are induced subgraphs of singular configurations, the latter occurring as induced subgraphs of ?$G$?. We show that there exists a set of ?$\eta$? distinct vertices representing the singular configurations. We also explore how the nullity controls the size of the singular substructures and characterize those graphs of maximal nullity containing a substructure reaching maximal sizeTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije