Counting One-Vertex Maps
Alen Orbanic, Marko Petkovsek, Tomaz Pisanski, Primoz Potocnik

TL;DR
This paper calculates the number of unique one-vertex maps with various configurations, considering different graph types such as signed, unsigned, directed, or undirected, for any valence d.
Contribution
It provides a comprehensive enumeration of one-vertex maps across multiple graph types, extending previous work to include signed and directed cases.
Findings
Derived formulas for counting maps with a single vertex and given valence.
Enumerated maps for both signed and unsigned, directed and undirected graphs.
Established a general method applicable to various map types.
Abstract
The number of distinct maps (pre-maps) with a single vertex and valence is computed for any value of . The types of maps (pre-maps) that we consider depend on whether the underlaying graph (pre-graph) is signed or unsigned and directed or undirected.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Data Management and Algorithms · Computational Geometry and Mesh Generation
