Counting rooted 4-regular unicursal planar maps

Counting rooted 4-regular unicursal planar maps

A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters: the number of edges, the number of inner faces and the valencies o...

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Veröffentlicht in:Acta Mathematicae Applicatae Sinica 2017-10, Vol.33 (4), p.909-918
Hauptverfasser: Long, Shu-de, Cai, Jun-liang
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Zusammenfassung:A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters: the number of edges, the number of inner faces and the valencies of the two odd vertices.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-017-0706-x