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- Publisher
- Wiley
- Copyright
- Copyright © 2018 Wiley Subscription Services, Inc., A Wiley Company
- ISSN
- 0108-7673
- eISSN
- 1600-5724
- DOI
- 10.1107/S2053273318002036
- pmid
- 29724968
- Publisher site
- See Article on Publisher Site
Abstract
This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius–Kantor graph on the torus, the genus‐2 bitorus and the genus‐3 tritorus, as well as the two‐dimensional, 7‐valent Klein graph on the tritorus (and its dual: the 3‐valent Klein graph). The genus‐2 and ‐3 embeddings describe quotient graphs of 2‐ and 3‐periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius–Kantor and 7‐valent Klein graphs.
Journal
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: May 1, 2018
Keywords: ; ;