Surface embeddings of the Klein and the Möbius–Kantor graphs

Research output: Contribution to journalJournal articlepeer-review

  • Martin Cramer Pedersen
  • Olaf Delgado-Friedrichs
  • Stephen T. Hyde

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 languageEnglish
JournalActa Crystallographica Section A: Foundations and Advances
Volume74
Issue number3
Pages (from-to)223-232
Number of pages10
ISSN0108-7673
DOIs
Publication statusPublished - May 2018
Externally publishedYes

    Research areas

  • Klein graph, Möbius–Kantor graph, periodic nets

ID: 229370489