  The $\alpha$-spectral radius of a connected graph $G$ is the spectral radius
of $A_\alpha$-matrix of $G$. In this paper, we discuss the methods for
comparing $\alpha$-spectral radius of graphs. As applications, we characterize
the graphs with the maximal $\alpha$-spectral radius among all unicyclic and
bicyclic graphs of order $n$ with diameter $d$, respectively. Finally, we
determine the unique graph with maximal signless Laplacian spectral radius
among bicyclic graphs of order $n$ with diameter $d$.
