Note
Almost Moore digraphs are diregular

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Abstract

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.

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Research done while the second and third authors were visiting the Department of Computer Science and Software Engineering of the University of Newcastle NSW Australia, supported by small ARC grant.