Surface embeddings of the Klein and the Möbius–Kantor graphs
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Surface embeddings of the Klein and the Möbius–Kantor graphs. / Pedersen, Martin Cramer; Delgado-Friedrichs, Olaf; Hyde, Stephen T.
I: Acta Crystallographica Section A: Foundations and Advances, Bind 74, Nr. 3, 05.2018, s. 223-232.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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.
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
UR - http://www.scopus.com/inward/record.url?scp=85046535971&partnerID=8YFLogxK
U2 - 10.1107/S2053273318002036
DO - 10.1107/S2053273318002036
M3 - Journal article
C2 - 29724968
AN - SCOPUS:85046535971
VL - 74
SP - 223
EP - 232
JO - Acta Crystallographica Section A: Foundations and Advances
JF - Acta Crystallographica Section A: Foundations and Advances
SN - 0108-7673
IS - 3
ER -
ID: 229370489