IJPAM: Volume 78, No. 3 (2012)

CLASSIFICATION OF REGULAR DIGRAPHS,
NORMALLY REGULAR DIGRAPHS,
AND STRONGLY REGULAR DIGRAPHS

Abdullah Al-Azemi
Department of Mathematics
Faculty of Science
Kuwait University
P.O. Box 5969, Safat, 13060, KUWAIT


Abstract. 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 in-neighbors. The second type is the class of normally regular digraphs introduced by Jørgensen. In these digraphs, the number of common out-neighbors (or in-neighbors) 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.

Received: February 2, 2012

AMS Subject Classification: 05C20, 05C30

Key Words and Phrases: digraph, regular digraph, normally regular digraph, strongly regular digraph, doubly regular tournament

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 3