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    • Diregularity of digraphs of out-degree three and order two less than Moore bound 

      Slamin; Miller, M.; Baskoro, E. T. (Proceeding of 12th Australasian Workshop on Combinatorial Algorithms, 2001)
      It is easy to show that any digraph with out-degree at most $d \ge 2$, diameter $k \ge 2$ and order $n=d+d^2+\dots + d^k - 1$, that is, two less than Moore bound must have all vertices of out-degree $d$. In other words, ...