Nonexistence of almost Moore digraphs of diameter four

Abstract

Regular digraphs of degree d > 1, diameter k > 1 and order N(d; k) = d+ +dk will be called almost Moore (d; k)-digraphs. So far, the problem of their existence has only been solved when d = 2; 3 or k = 2; 3. In this paper we prove that almost Moore digraphs of diameter 4 do not exist for any degree dPostprint (published version