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Arc‐transitive maps with underlying Rose Window graphs
Author(s) -
Hubard Isabel,
RamosRivera Alejandra,
Šparl Primož
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22608
Subject(s) - transitive relation , combinatorics , mathematics , transitive reduction , arc (geometry) , transitive closure , automorphism , graph , symmetric graph , discrete mathematics , line graph , voltage graph , geometry
In the late 1990s, Graver and Watkins initiated the study of all edge‐transitive maps. Recently, Gareth Jones revisited the study of such maps and suggested classifying the maps in terms of either their automorphism groups or their underlying graphs. A natural step towards classifying edge‐transitive maps is to study the arc‐transitive ones. In this paper, we investigate the connection of a class of arc‐transitive maps to consistent cycles of the underlying graph, with special emphasis on maps of smallest possible valence, namely 4. We give a complete classification of arc‐transitive maps whose underlying graphs are arc‐transitive Rose Window graphs.