Vladimir Kirichenko
Kiev National Taras Shevchenko University, Ukraine
Spectra of simple graphs.
Abstract: Let G be a finite undirected graph without loops and multiplied edges. We give a proof of the following known theorem: A connected graph G has an index r_G < 2 if and only if G is one of Dynkin-graphs: A_n, D_n, E_6, E_7, E_8. G has an index r_G = 2 if and only if G is one of extended Dynkin-graphs: \tilde{A_n}, \tilde{D_n}, \tilde{E_6}, \tilde{E_7}, \tilde{E_8}.