Regular maps from Cayley graphs. II: Antibalanced Cayley maps
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.
scientific article; zbMATH DE number 500618