Thanks a lot, but I don't see the absurdity in the fact that if the diameter is greater than $2,$ then we're obliged to have more eigenvalues.

Problem $26$: Suppose that a connected graph $G$ has only two distinct eigenvalues. Prove that

$G$ is the complete graph.

$[$ Hint $($to be read backwards$)$: $?$hparg eht fo retemaid eht tuoba yas uoy nac tahW $]$