Geodesic
The Enumeration of Non-Isomorphic 2-Connected Planar Maps
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 417-435

Voir la notice de l'article provenant de la source Cambridge University Press

Since Tutte initiated the systematic enumeration of planar maps [11], most of the literature on the subject has dealt with rooted maps (i.e., with maps whose automophism group has been trivialized by distinguishing a doubly-oriented edge). In particular, Tutte proved [11] that the number B′(n) of rooted planar 2-connected (i.e., non-separable) maps with n ≧ 1 edges is expressed by the formula Recently one of the authors developed a general technique for enumerating unrooted planar maps considered up to orientationpreserving isomorphisms (see [6] and [8]). This technique, which is based on combinatorial map theory, Burnside’s lemma [3, p. 181] and the concept of a quotient map (see Section 1.4), was used to find, with little algebraic manipulation, simple counting formulae for the numbers of non-isomorphic planar maps of several types [7]. 
Liskovets, V. A.; Walsh, T. R. S. The Enumeration of Non-Isomorphic 2-Connected Planar Maps. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 417-435. doi: 10.4153/CJM-1983-023-5
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