Isomorphism Classes of Vertex-Transitive Tournaments
Stefan Zetzsche

TL;DR
This paper derives a formula for counting isomorphism classes of vertex-transitive tournaments of prime order, introducing Cayley tournaments to establish a one-to-one correspondence.
Contribution
It provides a new formula for the number of such classes and introduces Cayley tournaments as a key concept for classification.
Findings
Established a one-to-one correspondence between vertex-transitive and Cayley tournaments of prime order.
Derived a formula for counting isomorphism classes of vertex-transitive tournaments.
Introduced Cayley tournaments as a subclass of Cayley digraphs.
Abstract
Tournaments are graphs obtained by assigning a direction for every edge in an undirected complete graph. We give a formula for the number of isomorphism classes of vertex-transitive tournaments with prime order. For that, we introduce Cayley tournaments, which are special Cayley digraphs, and show that there is a one to one identification between the isomorphism classes of vertex-transitive tournaments with prime order and the isomorphism classes of Cayley tournaments with prime order.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
