A note on enumeration of one-vertex maps - Orbanić, Alen (Ars mathematica contemporanea, 2010)
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: matematika; teorija grafov