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In this paper we show that two distinct conjectures, the first proposed byBabai and Godsil in $1982$ and the second proposed by Xu in $1998$, concerningthe asymptotic enumeration of Cayley graphs are in fact equivalent. This resultfollows from a more general theorem concerning the asymptotic enumeration of acertain family of Cayley graphs.

On the equivalence between a conjecture of Babai-Godsil and a conjecture of Xu concerning the enumeration of Cayley graphs