A note on enumeration of one-vertex maps

Alen Orbanić, Marko Petkovšek, Tomaž Pisanski, Primož Potočnik

Abstract


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.

Keywords


map, pre-map, graph, pre-graph, Cayley map

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DOI: https://doi.org/10.26493/1855-3974.95.a7b

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications