381 KB39 KB200820252014Jang, Hye JinKoolen, JackMunemasa, AkihiroTaniguchi, Tetsujištevilka:1letnik:7str. 105-121COBISSID:16793689ISSN:1855-3966URN:URN:NBN:SI:doc-61D8K5TXenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneagraph eigenvalueHoffman graphline graphroot systemspecial graphteorija grafovOn fat Hoffman graphs with smallest eigenvalue at least -3|We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph ?$S(\mathfrak{H})$? of an indecomposable fat Hoffman graph ?$\mathfrak{H}$? is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph ?$S^-(\mathfrak{H})$? is isomorphic to one of the Dynkin graphs ?$A_n$?, ?$D_n$?, or extended Dynkin graphs ?$\tilde{A}_n$? or ?$\tilde{D}_n$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije