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.

Rights

URN

URN:NBN:SI:DOC-R17TQ25P

COBISSID

188232195

DOI

10.26493/2590-9770.1617.83c

Added

11.04.2024

Metadata

Citation

APA:

Berman, Leah, Koike Quintanar, Sergio Hiroki, Mochán, Elías, Ramos Rivera, Alejandra, Šparl, Primož, Wilson, Steve (2023). Symmetries of the Woolly Hat graphs. The art of discrete and applied mathematics, volume 7, issue 2, 24 str. URN:NBN:SI:DOC-R17TQ25P from http://www.dlib.si

MLA:

Berman, Leah, Koike Quintanar, Sergio Hiroki, Mochán, Elías, Ramos Rivera, Alejandra, Šparl, Primož, Wilson, Steve. "Symmetries of the Woolly Hat graphs." The art of discrete and applied mathematics volume 7. issue 2 (2023) 24 str..
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-R17TQ25P>