Journal for Geometry and Graphics 13 (2009), No. 1, 001--013
Copyright Heldermann Verlag 2009
Regular Colour-Preserving Coverings of Low Genus of the Face-Colored Hemicube
Antonio Breda d'Azevedo
Dept. of Matematics, University of Aveiro, 3810-193 Aveiro, Portugal
breda@ua.pt
Domenico Catalano
Dept. of Matematics, University of Aveiro, 3810-193 Aveiro, Portugal
domenico@ua.pt
Rui Duarte
Dept. of Matematics, University of Aveiro, 3810-193 Aveiro, Portugal
rduarte@ua.pt
We classify the Δ012-regular hypermaps of characteristic χ ≥ -2. We also define and compute the upper and lower irregularity group which are a generalization of the chirality group. From the obtained classification it follows that there is no edge-transitive map of characteristic χ ≥ -2 and type 5P.
Keywords: Maps, hypermaps, embeddings of graphs and hypergraphs, restricted regularity of hypermaps, chirality.
MSC: 05C10; 05C25, 20B25, 20F65, 51E30, 57M60
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