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Edge-transitive maps and non-orientable surfaces. (English) Zbl 0958.05032
The paper presents two classifications of maps on surfaces such that their automorphism group acts transitively on edges. The first classification is based on the number and arrangement of orbits of flags under the action of the monodromy group (connection group) of the map. The other classification starts with classifying all the actions on a surface by a group whose order is larger than a certain minimum, and leads to the analysis of the shape of the fundamental region. Then the connection between the classifications is shown. It transpires that each case of the second classification can be interpreted and understood in terms of edge-transitive maps.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
57M15 Relations of low-dimensional topology with graph theory
57M60 Group actions on manifolds and cell complexes in low dimensions
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References:
[1] BREDA D’AZEVEDO A.: Hypermaps and Symmetry. Doctoral Thesis, Univ. of Southampton, 1991.
[2] BREDA D’AZEVEDO A.-WILSON S.: Non-orientable surfaces which have no regular hypermaps. · Zbl 1033.05029
[3] CONDER M.-MacLACHLAN C.-WILSON S.: Lower bounds on largest groups on non-orientable surfaces.
[4] CORN D.-SINGERMAN D.: Regular hypermaps. European J. Combin. 9 (1988), 337-351. · Zbl 0665.57002
[5] MacLACHLAN C.: A bound for the number of automorphisms of a compact Riemann surface. J. Lond. Math. Soc. 44 (1969), 265-272. · Zbl 0164.37904
[6] SINGERMAN D.: Symmetries of Riemann surfaces with large automorphism groups. Math. Ann. 210 (1974), 17-32. · Zbl 0272.30022
[7] WILSON S.: Operators over regular maps. Pacific J. Math. (1979), 559-568. · Zbl 0433.05021
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