Spectral radius of strongly connected digraphs

Let $D$ be a digraph with vertex set $V\left(D\right)$ and $A$ be the adjacency matrix of $D$. The largest eigenvalue of $A$, denoted by $\rho \left(D\right)$, is called the spectral radius of the digraph $D$. In this paper, we establish some sharp upper or lower bounds for digraphs with some given graph parameters, such as clique number, girth, and vertex connectivity, and characterize the corresponding extremal graphs. In addition, we give the exact value of the spectral radii of those digraphs.