In this theses , first we investigate to the structure of minimum vertex and edge cuts of distance-regular digraphs . We show that each distance-regular digraph $\\Gamma$ , different from an undirected cycle , is super edge-connected , i.e . any minimum edge cut of $\\Gamma$ is the set of all edges going into (or coming out of) a single vertex . Moreover , we will show that except undirected cycles , any distance regular-digraph $\\Gamma$ with diameter $D=?$ , degree $k\\leq ?$ or $\\lambda=?$ ($\\lambda$ is the number of ?-paths from $u$ to $v$ for an edge $uv$ of $\\Gamma$) is super vertex-connected , i.e . any minimum vertex cut of $\\Gamma$ is the set of all out-neighbors (or in-neighbors) of a single vertex in $\\Gamma$ .
