A problem on algebraic graph theory (Q1062995)

Two trees with ten vertices are presented. Both of them have characteristic polynomial insolvable by radicals. This result answers the seventh open problem in the book ''Spectra of Graphs'' (1982; Zbl 0458.05042), raised by \textit{D. M. Cvetkovic}, \textit{M. Doob} and \textit{H. Sachs}. In the paper ''The minimal graphs with characteristic polynomial insolvable by radicals'' [Kexue Tongbao, Foreign Lang. Ed. 30, 1299-1302 (1985)] the author presents two graphs of six vertices with the same property.