Miller, Mirka; Gimbert, Joan; Širáň, Jozef and Slamin, S.
Almost Moore digraphs are diregular.
Discrete Mathematics, 218(1-3) pp. 265–270.
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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