Surface embeddings of the Klein and the Möbius–Kantor graphs
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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.
Original language | English |
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Journal | Acta Crystallographica Section A: Foundations and Advances |
Volume | 74 |
Issue number | 3 |
Pages (from-to) | 223-232 |
Number of pages | 10 |
ISSN | 0108-7673 |
DOIs | |
Publication status | Published - May 2018 |
Externally published | Yes |
- Klein graph, Möbius–Kantor graph, periodic nets
Research areas
ID: 229370489