2 problems

Let $k\geq 2$ and let $m$ be sufficiently large. For a graph $G$, write $\rho(G)$ for its spectral radius, let $H_{r}$ denote the fan graph with $r$ vertices, let $K_k$ be the comp…

Let $G$ be a graph with $m$ edges, and let $lambda(G)$ denote its spectral radius. For an integer $k$, write $F_l$ for the fan graph obtained by joining an isolated vertex to the p…