Classification of Regular Digraphs, Normally Regular Digraphs, and Strongly Regular Digraphs
نویسندگان
چکیده
We use an exhaustive generation with isomorph-rejection to classify three types of structured digraphs. The first type is the class of regular digraphs where each vertex has the same number of out-neighbors and inneighbors. The second type is the class of normally regular digraphs introduced by Jørgensen. In these digraphs, the number of common out-neighbors (or inneighbors) of vertices x and y depends only on whether they are adjacent. We observe some remarks on the order of the automorphism group on some of those digraphs. Also, we make some improvements in the table of results of Jørgensen’s search. The thrid type is the class of strongly regular digraphs introduced by Duval. In those digraphs, the number of directed paths of length 2 from vertex x to vertex y depends only on whether x dominates y. Our results on those digraphs were on full agreement with those of Duval and Jørgensen. AMS Subject Classification: 05C20, 05C30
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