# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Classification of edge-transitive maps

Presented by Mr. Ján KARABáš
Type: Oral presentation
Track: Maps and Symmetries

## Content

An orientable map is edge-transitive if and only if its medial is a vertex-transitive map. Applying the techniques of classification and construction of vertex-transitive maps we obtain a classification of edge-transitive maps. Since the orientation-preserving automorphism group is of index at most two in the automorphism group of a map we know, that the quotient of the medial map has at most two vertices. The lifting technique can be used for the construction. Orientation-preserving automorphisms of an edge-transitive map are \emph{face colour-preserving}, i. e. they cannot act as a duality in the medial map. The number of possible quotient maps significantly decreases, in particular there are just six quotient maps to consider These gives to rise to \emph{six} infinite families of edge-transitive maps. Using techniques of voltage assignments we can reconstruct all edge-transitive maps of given genus or up to given number of edges.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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