Minimum Cuts of Distance-Regular Digraphs

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph Γ, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of Γ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular-digraph Γ with diameter D = 2, degree k 6 3 or λ = 0 (λ is the number of 2-paths from u to v for an edge uv of Γ) is super vertex-connected, that is, any minimum vertex cut of Γ is the set of all out-neighbors (or in-neighbors) of a single vertex in Γ. These results extend the same known results for the undirected case with quite different proofs.