A note on enumeration of one-vertex maps

Authors

  • Alen Orbanić
  • Marko Petkovšek
  • Tomaž Pisanski University of Ljubljana
  • Primož Potočnik

DOI:

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

Keywords:

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

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.

Published

2009-12-24

Issue

Section

Articles