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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, Volume 28, Number 2, Pages 274–296
DOI: https://doi.org/10.21538/0134-4889-2022-28-2-274-296 (Mi timm1921) 		 
The girths of the cubic pancake graphs

Elena V. Konstantinovaab, Son En Gunb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.21538/0134-4889-2022-28-2-274-296
Abstract: The pancake graphs $P_n, n\geqslant 2$, are Cayley graphs over the symmetric group $\mathrm{Sym}_n$ generated by prefix-reversals. There are six generating sets of prefix-reversals of cardinality three which give connected Cayley graphs over the symmetric group known as cubic pancake graphs. In this paper we study the girth of the cubic pancake graphs. It is proved that considered cubic pancake graphs have the girths at most twelve.
Keywords: pancake graph; cubic pancake graph; prefix-reversal; girth.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0017
075-15-2022-281
The first author is supported by the project No. FWNF-2022-0017 (the state contract of the Sobolev Institute of Mathematics). The second author is partially supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 30.12.2021
Revised: 01.03.2022
Accepted: 10.03.2022
Bibliographic databases:
Document Type: Article
MSC: 05C25, 05C38, 05C82, 68R10
Language: English
Citation: Elena V. Konstantinova, Son En Gun, “The girths of the cubic pancake graphs”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 2, 2022, 274–296
Citation in format AMSBIB
\Bibitem{KonGun22}
\by Elena~V.~Konstantinova, Son~En~Gun
\paper The girths of the cubic pancake graphs
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2022
\vol 28
\issue 2
\pages 274--296
\mathnet{http://mi.mathnet.ru/timm1921}
\crossref{https://doi.org/10.21538/0134-4889-2022-28-2-274-296}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4453874}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000905209900022}
\elib{https://elibrary.ru/item.asp?id=48585967}
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