Surface embeddings of the Klein and the Möbius–Kantor graphs (2024)

Pedersen, M. C., Delgado-Friedrichs, O., & Hyde, S. T. (2018). Surface embeddings of the Klein and the Möbius–Kantor graphs. Acta Crystallographica Section A: Foundations and Advances, 74(3), 223-232. https://doi.org/10.1107/S2053273318002036

Pedersen, Martin Cramer ; Delgado-Friedrichs, Olaf ; Hyde, Stephen T. / Surface embeddings of the Klein and the Möbius–Kantor graphs. In: Acta Crystallographica Section A: Foundations and Advances. 2018 ; Vol. 74, No. 3. pp. 223-232.

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title = "Surface embeddings of the Klein and the M{\"o}bius–Kantor graphs",

abstract = "This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the M{\"o}bius–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 M{\"o}bius–Kantor and 7-valent Klein graphs.",

keywords = "Klein graph, M{\"o}bius–Kantor graph, periodic nets",

author = "Pedersen, {Martin Cramer} and Olaf Delgado-Friedrichs and Hyde, {Stephen T.}",

note = "Publisher Copyright: {\textcopyright} International Union of Crystallography, 2018",

year = "2018",

month = may,

doi = "10.1107/S2053273318002036",

language = "English",

volume = "74",

pages = "223--232",

journal = "Acta Crystallographica Section A: Foundations and Advances",

issn = "0108-7673",

publisher = "John Wiley & Sons Inc.",

number = "3",

}

Pedersen, MC, Delgado-Friedrichs, O & Hyde, ST 2018, 'Surface embeddings of the Klein and the Möbius–Kantor graphs', Acta Crystallographica Section A: Foundations and Advances, vol. 74, no. 3, pp. 223-232. https://doi.org/10.1107/S2053273318002036

Surface embeddings of the Klein and the Möbius–Kantor graphs. / Pedersen, Martin Cramer; Delgado-Friedrichs, Olaf; Hyde, Stephen T.
In: Acta Crystallographica Section A: Foundations and Advances, Vol. 74, No. 3, 05.2018, p. 223-232.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Surface embeddings of the Klein and the Möbius–Kantor graphs

AU - Pedersen, Martin Cramer

AU - Delgado-Friedrichs, Olaf

AU - Hyde, Stephen T.

N1 - Publisher Copyright:© International Union of Crystallography, 2018

PY - 2018/5

Y1 - 2018/5

N2 - 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.

AB - 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.

KW - Klein graph

KW - Möbius–Kantor graph

KW - periodic nets

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U2 - 10.1107/S2053273318002036

DO - 10.1107/S2053273318002036

M3 - Article

SN - 0108-7673

VL - 74

SP - 223

EP - 232

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

IS - 3

ER -

Pedersen MC, Delgado-Friedrichs O, Hyde ST. Surface embeddings of the Klein and the Möbius–Kantor graphs. Acta Crystallographica Section A: Foundations and Advances. 2018 May;74(3):223-232. doi: 10.1107/S2053273318002036