ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 24 (2024) #P2.02
https://doi.org/10.26493/1855-3974.2896.7e6
(Also available at http://amc-journal.eu)
Algebraic degrees of 2-Cayley digraphs over
abelian groups*
Yongjiang Wu, Jing Yang, Lihua Feng †
School of Mathematics and Statistics, HNP-LAMA, Central South University,
Changsha, Hunan, 410083, P.R. China
Received 3 June 2022, accepted 22 March 2023, published online 8 September 2023
Abstract
A digraph Γ is called a 2-Cayley digraph over a group G if there exists a 2-orbit
semiregular subgroup of Aut(Γ) isomorphic to G. In this paper, we completely deter-
mine the algebraic degrees of 2-Cayley digraphs over abelian groups. This generalizes the
main results of Lu and Mönius in 2023. As applications, we consider the algebraic degrees
of Cayley digraphs over finite groups admitting an abelian subgroup of index 2. Special
attention is paid to the algebraic degrees of Cayley (di)graphs over generalized dihedral
groups, generalized dicyclic groups and semi-dihedral groups.
Keywords: Algebraic degree, 2-Cayley digraph, Abelian group.
Math. Subj. Class. (2020): 05C25, 05C50
*This research was supported by NSFC (Nos. 12271527, 12071484), Hunan Provincial Natural Science Foun-
dation (2020JJ4675, 2018JJ2479). The authors would like to express their sincere thanks to the referee for the
valuable suggestions which greatly improved the presentation of the original manuscript.
†Corresponding author.
E-mail addresses: su15273815046@163.com (Yongjiang Wu), yj1147943429@163.com (Jing Yang),
fenglh@163.com (Lihua Feng)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 1855-3966 (tiskana izd.), ISSN 1855-3974 (elektronska izd.)
ARS MATHEMATICA CONTEMPORANEA 24 (2024) #P2.02
https://doi.org/10.26493/1855-3974.2896.7e6
(Dostopno tudi na http://amc-journal.eu)
Algebraične stopnje 2-Cayleyjevih digrafov
abelskih grup*
Yongjiang Wu, Jing Yang, Lihua Feng †
School of Mathematics and Statistics, HNP-LAMA, Central South University,
Changsha, Hunan, 410083, P.R. China
Prejeto 3. junija 2022, sprejeto 22. marca 2023, objavljeno na spletu 8. septembra 2023
Povzetek
Digraf Γ se imenuje 2-Cayleyjev digraf grupe G, če obstaja 2-orbitna semiregularna
podgrupa Aut(Γ), izomorfna G. V tem članku v celoti določimo algebraične stopnje 2-
Cayleyjevih digrafov abelskih grup. To je posplošitev glavnih rezultatov Luja in Möniusa
iz leta 2023. Kot aplikacije obravnavamo algebraične stopnje Cayleyjevih digrafov končnih
grup, ki dopuščajo abelsko podgrupo indeksa 2. Posebno pozornost namenjamo alge-
braičnim stopnjam Cayleyjevih (di)grafov posplošenih diedrskih grup, posplošenih dicik-
ličnih grup in semidiedrskih grup.
Ključne besede: Algebraična stopnja, 2-Cayleyjev digraf, abelska grupa.
Math. Subj. Class. (2020): 05C25, 05C50
*To raziskava je podprla NSFC (št. 12271527, 12071484), Hunan Provincial Natural Science Foundation
(2020JJ4675, 2018JJ2479). Avtorji bi se radi iskreno zahvalili recenzentu za dragocene predloge, ki so močno
izboljšali predstavitev prvotnega rokopisa.
†Kontaktni avtor.
E-poštni naslovi: su15273815046@163.com (Yongjiang Wu), yj1147943429@163.com (Jing Yang),
fenglh@163.com (Lihua Feng)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/