is the graph $G$ determine unique by the eigenvalue?

Question

the graph $G$ have eigenvalue 2, 1, 0, -1 and -2 and frequent of the eigenvalue Respectively 1, 2, 1, 2 and 1. is the graph $G$ determine unique by the eigenvalue?

Answer 1

It’s not determined by its spectrum. It’s cospectral with the union of $C_6$ and an isolated vertex.