Open AccessA note on enumeration of one-vertex maps
Author(s) -
Alen Orbanić,
Marko Petkovšek,
Tomaž Pisanski,
Primož Potočnik
Publication year - 2010
Publication title -
ars mathematica contemporanea
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.673
H-Index - 18
eISSN - 1855-3974
pISSN - 1855-3966
DOI - 10.26493/1855-3974.95.a7b
Subject(s) - enumeration , mathematics , combinatorics , vertex (graph theory) , graph , undirected graph , discrete mathematics
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.
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