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On labeled vertex-transitive digraphs with a prime number of vertices

✍ Scribed by Chong-Yun Chao; Jacqueline G. Wells

Publisher: Elsevier Science
Year: 1983
Tongue: English
Weight: 481 KB
Volume: 46
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90126-7

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✦ Synopsis

We enumerate, up to isomorphism, several classes of labeled vertex-transitive digraphs with a prime number of vertices.

There are many unsolvedi enumeration problems stated in [S]. Recently, Robinson in [8] posed more enumeration problems. Here, we give some partial answer to the problems posed on p. 181 in [S], i.e., bj using some of the results in [3] and [4], we enumerate several classes of labeled vertex-transitive digraphs with a prime number, p, of vertices; specifically, we count those that are symmetric (both vertex-tracsitive and edge-transitive), those with a given group of automorphisms and those that are self-complementary.

Roughly, our method is to use the group of automorphisms, P6lya's and de Bruijn's enumeration theorems and the following lemma.

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