Some Conditions for the Existence of ( d, k)-Digraphs

A (d,k)-digraph is a diregular digraph of degree d ≥ 4, diameter k ≥ 3 and the number of vertices d+d2+...+dk. The existence problem of (d,k)-digraphs is one of difficult problem. In this paper, we will present some new necessary conditions for the existence of such digraphs.