286 KB26 KB200820252016Mednykh, AlexanderMednykh, Ilyaletnik:10številka:2str. 223-235COBISSID:17830745ISSN:1855-3966URN:URN:NBN:SI:doc-KLE2RACDenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneagrafgraphisospectral graphsizospektralni grafiLaplaceov polinomLaplaceov spekterLaplacian polynomialLaplacian spectrumspanning treevpeto drevoIsospectral genus two graphs are isomorphic|By a graph we mean a finite connected multigraph without bridges. The genus of a graph is the dimension of its homology group. Two graphs are isospectral is they share the same Laplacian spectrum. We prove that two genus two graphs are isospectral if and only if they are isomorphic. Also, we present two bridgeless genus three graphs that are not isomorphic. The paper is motivated by the following open problem posed by Peter Buser: are isospectral Riemann surfaces of genus two isometric?Graf nam v tem članku pomeni: končen povezan multigraf brez mostov, rod grafa pa: dimenzijo njegove homološke grupe. Dva grafa sta izospektralna, če si delita isti Laplaceov spekter. Dokažemo, da sta dva grafa roda 2 izospektralna natanko tedaj, ko sta izomorfna. Predstavimo tudi dva brezmostna grafa roda 3, ki pa nista izomorfna. Motivacija za ta članek je bil naslednji odprti problem, ki ga je zastavil Peter Buser: Ali so izospektralne Riemannove ploskve roda 2 izometrične?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije