Almost Moore digraphs are diregular

An almost Moore digraph is a digraph of diameter k⩾2, maximum out-degree d⩾2 and order n=d+d2+⋯+dk, that is, one less than the Moore bound. It is easy to show that the out-degree of an almost Moore digraph is constant (=d). In this note we prove that also the in-degree of an almost Moore digraph is constant (=d), that is, every almost Moore digraph is diregular of degree d.