0 KB211 KB16 KB200820252012Levit, Vadim E.Mandrescu, Eugenštevilka:2letnik:5str. 325-331COBISSID:16277849ISSN:1855-3966URN:URN:NBN:SI:doc-NC5HFPJDenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneacoreenociklični grafgraph theoryjedro grafaKönig-Egervárijev grafKönig-Egerváry graphmaksimalna neodvisna množicamatchingmaximum independent setprirejanjeteorija grafovunicyclic graphOn the core of a unicyclic graph|A set ?$S \subseteq V$? is independent in a graph ?$G = (V, E)$? if no two vertices from ?$S$? are adjacent. By core?$(G)$? we mean the intersection of all maximum independent sets. The independence number ?$\alpha(G)$? is the cardinality of a maximum independent set, while ?$\mu(G)$? is the size of a maximum matching in ?$G$?. A connected graph having only one cycle, say ?$C$?, is a unicyclic graph. In this paper we prove that if ?$G$? is a unicyclic graph of order ?$n$? and T$n - 1 = \alpha(G) + \mu(G)$T, then core?$(G)$? coincides with the union of cores of all trees in ?$G - C$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije