Connected graphs having maximum signless Laplacian spectral radius
Let $\rho(G)$ denote the signless Laplacian spectral radius of a graph $G$, and let $\mathcal C_{n,m}$ be the family of connected graphs of order $n$ and size $m$. A graph is $Q$-maximal if it maximizes $\rho(G)$ over this family. Motivated by a question of Chang and Tam (2011), we study this extremal problem using sca...