Kan Hu (Author), Roman Nedela (Author), Martin Škoviera (Author), Naer Wang (Author)

Abstract

Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.

Keywords

regularna vložitev;večkratna povezava;Hölderjev izrek;Möbiusov zemljevid;regular embedding;multiple edge;Hölder's Theorem;Möbius map;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UP - University of Primorska
UDC: 519.17:512.54
COBISS: 1537209540 Link will open in a new window
ISSN: 1855-3966
Parent publication: Ars mathematica contemporanea
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Other data

Secondary language: Unknown
Secondary abstract: Regular embeddings of cycles with multiple edges have been reappearing in the literature for quite some time, both in and outside topological graph theory. The present paper aims to draw a complete picture of these maps by providing a detailed description, classification, and enumeration of regular embeddings of cycles with multiple edges on both orientable and non-orientable surfaces. Most of the results have been known in one form or another, but here they are presented from a unique viewpoint based on finite group theory. Our approach brings additional information about both the maps and their automorphism groups, and also gives extra insight into their relationships.
Type (COBISS): Not categorized
Pages: str. 177-194
Volume: ǂVol. ǂ8
Issue: ǂno. ǂ1
Chronology: 2015
DOI: 10.26493/1855-3974.626.f9d
ID: 9058027