2 problems

Let $\varepsilon=\frac{1}{3}\left((54 - 6\sqrt{33})^{\frac{1}{3}} + (54 + 6\sqrt{33})^{\frac{1}{3}} \right)$, and let $\rho_Q(G)$ denote the signless Laplacian spectral radius of a…

Let $\omega = \frac{1}{3}\left((19 + 3\sqrt{33})^{\frac{1}{3}} + (19 - 3\sqrt{33})^{\frac{1}{3}}+1 \right)$, and let $\rho_L(G)$ denote the Laplacian spectral radius of a graph $G$…