Geodesic
A note on enumeration of one-vertex maps
Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 1-12.

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Explicit formula for the numbers of distinct maps and pre-maps having a single vertex of valence d are given. The question of what precisely is meant by a map can be answered in several different ways. We enumerate 16 different types of objects where each type is obtained by selecting whether the object is a pre-map or a map, is oriented or general, whether the underlying graph or pre-graph is signed or unsigned, is directed or undirected.
DOI : 10.26493/1855-3974.95.a7b
Keywords: map, pre-map, graph, pre-graph, Cayley map 
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Alen Orbanić; Marko Petkovšek; Tomaž Pisanski; Primož Potočnik. A note on enumeration of one-vertex maps. Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 1-12. doi : 10.26493/1855-3974.95.a7b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.95.a7b/

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