Properties of mixed Moore graphs of directed degree one
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Mixed graphs of order n such that for any pair of vertices there is a unique trail of length at most k between them are known as mixed Moore graphs. These extremal graphs may only exist for diameter k = 2 and certain (infinitely many) values of n. In this paper we give some properties of mixed Moore
graphs of directed degree one and reduce their existence to the existence of some (undirected) strongly regular graphs.