In this paper we show that two distinct conjectures, the first proposed by Babai and Godsil in 1982 and the second proposed by Xu in 1998, concerning the asymptotic enumeration of Cayley graphs are in fact equivalent. This result follows from a more general theorem concerning the asymptotic enumeration of a certain family of Cayley graphs.
Spiga, P. (2021). On the equivalence between a conjecture of Babai-Godsil and a conjecture of Xu concerning the enumeration of Cayley graphs. THE ART OF DISCRETE AND APPLIED MATHEMATICS, 4(1), 1-10 [10.26493/2590-9770.1338.0b2].
On the equivalence between a conjecture of Babai-Godsil and a conjecture of Xu concerning the enumeration of Cayley graphs
Spiga P.
Primo
2021
Abstract
In this paper we show that two distinct conjectures, the first proposed by Babai and Godsil in 1982 and the second proposed by Xu in 1998, concerning the asymptotic enumeration of Cayley graphs are in fact equivalent. This result follows from a more general theorem concerning the asymptotic enumeration of a certain family of Cayley graphs.
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