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What is the number of non-isomorphic $2n$ vertex balanced bipartite graphs of degree at most $d$ and genus $g$?

I am most interested in $d\leq3$ and $g=0$.

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Closely related questions are considered in [

Guillaume Chapuy, Éric Fusy, Omer Giménez, Bojan Mohar, and Marc Noy, MR 2745423 Asymptotic enumeration and limit laws for graphs of fixed genus, J. Combin. Theory Ser. A 118 (2011), no. 3, 748--777.]1

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