Projects per year
Abstract
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges and even otherwise. Pontus von Brömssen (né Andersson) showed that the existence of such an automorphism is independent of the orientation and considered the question of counting pairwise nonisomorphic even graphs. Based on computational evidence, he made the rather surprising conjecture that the number of pairwise nonisomorphic even graphs on n vertices is equal to the number of pairwise nonisomorphic tournaments on n vertices. We prove this conjecture using a counting argument with several applications of the Cauchy–Frobenius theorem.
Original language  English 

Pages (fromto)  515524 
Number of pages  10 
Journal  Journal of Algebraic Combinatorics 
Volume  57 
Issue number  2 
Early online date  29 Dec 2022 
DOIs  
Publication status  Published  Mar 2023 
Projects
 1 Finished

Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. & Niemeyer, A.
21/02/19 → 31/12/22
Project: Research