A classification of regular $t$-balanced Cayley maps on $mathbb{Z}_2$-extensions of a cyclic 2-group

Young Soo Kwon; Jihye Park

doi:10.4134/BKMS.b230156

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

QR
Code

Article

HOME

ALL ARTICLES

View

Bull. Korean Math. Soc. 2024; 61(5): 1175-1195

Online first article September 25, 2024 Printed September 30, 2024

https://doi.org/10.4134/BKMS.b230156

A classification of regular $t$-balanced Cayley maps on $mathbb{Z}_2$-extensions of a cyclic 2-group

Young Soo Kwon, Jihye Park

Yeungnam University; Yeungnam University

Abstract

Go to

Abstract

A Cayley map $\mathcal{M} = CM(G,X,p)$ is $t$-balanced if $p(x)^{-1} =

p^t(x^{-1})$ for all $x \in X$.

Conder et al. classified

the regular anti-balanced Cayley maps on abelian groups and Kwak

et al. classified the regular $t$-balanced Cayley maps on dihedral

groups and dicyclic groups.

Classifications of regular $t$-balanced Cayley maps on semi-dihedral groups and cyclic groups were done by Oh and the first author, respectively.

In this paper, we classify the regular

$t$-balanced Cayley maps on $\mathbb{Z}_2$-extensions of a cyclic

$2$-group.

Keywords: Cayley map, $t$-balanced Cayley map, $mathbb{Z}_2$-extensions of a cyclic group

MSC numbers: 05C10, 05C25

Supported by: The first author and the second author were supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B05048450) and (2021K2A9A2A11101586), respectively.