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Hubard, Isabel; Ramos‐Rivera, Alejandra; Šparl, Primož
Journal of graph theory, February 2021, 2021-02-00, 20210201, Letnik: 96, Številka: 2Journal Article
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.
