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Title:Symmetries of the Woolly Hat graphs
Authors:ID Berman, Leah (Author)
ID Koike Quintanar, Sergio Hiroki (Author)
ID Mochán, Elías (Author)
ID Ramos Rivera, Alejandra (Author)
ID Šparl, Primož (Author)
ID Wilson, Steve (Author)
Files:.pdf PDF - Presentation file, download (555,34 KB)
MD5: 680BD2717ABDA58A0B26110444946330
 
URL URL - Source URL, visit https://adam-journal.eu/index.php/ADAM/article/view/1617
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different "types" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one "type" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones.
Keywords:edge-transitive, vertex-transitive, tricirculant, Woolly Hat graphs
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2024
Year of publishing:2024
Number of pages:24 str.
Numbering:Vol. 7, no. 2, [article no.] P2.06
PID:20.500.12556/DiRROS-20518 New window
UDC:519.17
ISSN on article:2590-9770
DOI:10.26493/2590-9770.1617.83c New window
COBISS.SI-ID:188232195 New window
Note:
Publication date in DiRROS:07.10.2024
Views:409
Downloads:155
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:
BERMAN, Leah, KOIKE QUINTANAR, Sergio Hiroki, MOCHÁN, Elías, RAMOS RIVERA, Alejandra, ŠPARL, Primož and WILSON, Steve, 2024, Symmetries of the Woolly Hat graphs. The art of discrete and applied mathematics [online]. 2024. Vol. 7, no. 2,  P2.06. [Accessed 21 April 2025]. DOI 10.26493/2590-9770.1617.83c. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=20518
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Record is a part of a journal

Title:The art of discrete and applied mathematics
Publisher:Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:2590-9770
COBISS.SI-ID:290758912 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0285
Name:Algebra, diskretna matematika, verjetnostni račun in teorija iger
Funder:ARRS - Slovenian Research Agency
Project number:J1-2451
Name:Simetrija na grafih preko rigidnih celic
Funder:ARRS - Slovenian Research Agency
Project number:J1-3001
Name:Terwilligerjeva algebra grafa

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License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

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