Semicomplete multipartite weakly distance-regular digraphs

A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, Jørgensen et al. \cite{JG14} initiated the study of doubly regular team tournaments. As a natural extension, we introduce doubly regular team semicomplete multipartite digraphs and show that such digraphs fall into three types. Furthermore, we give a characterization of all semicomplete multipartite commutative weakly distance-regular digraphs.