Characterization and construction of Cayley graphs admitting regular Cayley maps
type: Item
instance of: scholarly article
title: Characterization and construction of Cayley graphs admitting regular Cayley maps
zbMATH Open document ID: 0861.05030
DOI: 10.1016/0012-365X(95)00076-9
published in: Discrete Mathematics
publication date: 1997-05-04T00:00:00Z
review text: This paper addresses the question of which Cayley graphs can be the underlying graph of a regular Cayley map. A Cayley map is an embedding of a Cayley graph into an orientable surface such that the cyclic ordering of the edges around each vertex is the same. The map is regular if its group of map-automorphisms is as large as possible (making it arc-transitive). In a previous paper the author characterized the regular Cayley maps as those Cayley maps having a ``rotary mapping.'' In this paper he uses that result to characterize the underlying Cayley graphs, first in terms of a graph-automorphism property and then in terms of the presentation (relations) for the associated finite group.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 943223
zbMATH Keywords: characterization
zbMATH Keywords: rotary mapping
zbMATH Keywords: Cayley map
zbMATH Keywords: Cayley graph
zbMATH Keywords: surface
zbMATH Keywords: presentation
author: Robert Jajcay
reviewed by: Albert J. Goodman
MaRDI profile type: Publication
cites work: Q5654065
cites work: Q3050438
cites work: Characterisation of Graphs which Underlie Regular Maps on Closed Surfaces
cites work: Regular orientable imbeddings of complete graphs
cites work: Theory of Maps on Orientable Surfaces
cites work: Automorphism groups of Cayley maps
cites work: On a new product of groups
cites work: On a construction of infinite families of regular Cayley maps
cites work: Regular maps from Cayley graphs. I: Balanced Cayley maps
cites work: Regular maps from Cayley graphs. II: Antibalanced Cayley maps
cites work: Q3885783
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description: scientific article; zbMATH DE number 943223