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Construction and enumeration of regular maps on the torus

โœ Scribed by Amos Altshuler

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
652 KB
Volume
4
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A construction is given for all the regular maps of type (3, 6} on the torus, with v vertices, v being any integer > 0. We also find bounds for the number of those maps, in particular for the case in which the maps contain "normal" Hamiltonian circuits. Using duality, the results may be applied for the maps of type {6, 3} too.

๐Ÿ“œ SIMILAR VOLUMES

Enumeration of 2 -connected Loopless 4 -
Enumeration of 2 -connected Loopless 4 -regular Maps on the Plane
โœ Han Ren; Yanpei Liu; Zhaoxiang Li ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 195 KB

In this paper rooted (near-) 4-regular maps on the plane are counted with respect to the root-valency, the number of edges, the number of inner faces, the number of non-root vertex loops, the number of non-root vertex blocks, and the number of multi-edges. As special cases, formulae of several types