the sharp upper bounds and the sharp lower bounds of the largest eigenvalues $lambda_1$, the least eigenvalue $lambda_n$, the second largest eigenvalue $lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.

We generalize the classical sharp bounds for largest eigenvalue of normalized Laplace operator, $\frac{N}{N-1}\leq \lambda_N\leq 2$, to case chemical hypergraphs.