Geodesic
Enumeration of regular maps on surfaces of a given genus
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VIII, Tome 450 (2016), pp. 74-108
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In the present work labelled and unlabelled $d$-regular maps on two-dimensional oriented surfaces of arbitrary genus $g$ are enumerated. The case of $d$-regular maps with a single face is considered separately in more detail. 
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E. C. Krasko; A. V. Omelchenko. Enumeration of regular maps on surfaces of a given genus. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VIII, Tome 450 (2016), pp. 74-108. http://geodesic.mathdoc.fr/item/ZNSL_2016_450_a5/

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