Regular maps from Cayley graphs. II: Antibalanced Cayley maps
type: Item
instance of: scholarly article
title: Regular maps from Cayley graphs. II: Antibalanced Cayley maps
zbMATH Open document ID: 0791.05031
DOI: 10.1016/0012-365X(94)90089-2
author: Jozef Širáň
author: Martin Škoviera
published in: Discrete Mathematics
publication date: 1994-06-28T00:00:00Z
review text: This paper is Part II of a series. In Part I [Discrete Math. 109, No. 1- 3, 265-276 (1992; Zbl 0782.05028)] the authors define a Cayley map \(\text{CM} (G, \Omega,p)\) for finite group \(G\), generating set \(\Omega\) (closed under inverses and not containing the identity), and cyclic permutation \(p\) of \(\Omega\), to be balanced if \(p (\omega^{-1})=(p(\omega))^{- 1}\), for all \(\omega\) in \(\Omega\). Conditions were given for a balanced Cayley map to be regular or reflexible, and the corresponding map automorphism groups were determined. In Part II similar results are obtained for antibalanced Cayley maps, where the condition is \(p(\omega^{-1})=(p^{-1} (\omega))^{-1}\). The results and their proofs are based on the theory of groups with sign structure.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 500618
zbMATH Keywords: Cayley map
zbMATH Keywords: balanced
zbMATH Keywords: regular
zbMATH Keywords: reflexible
zbMATH Keywords: automorphism groups
zbMATH Keywords: antibalanced
reviewed by: Arthur T. White
MaRDI profile type: Publication
cites work: Regular maps from Cayley graphs. I: Balanced Cayley maps
cites work: Groups with sign structure and their antiautomorphisms
cites work: Q3222857
cites work: Cantankerous maps and rotary embeddings of \(K_ n\)
full work available at URL: 0012-365x(94)90089-2
OpenAlex ID: W4212957300
description: scientific article; zbMATH DE number 500618