Datta, Basudeb and Maity, Dipendu (2017) Semiequivelar and vertextransitive maps on the torus. In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 58 (3). pp. 617634. ISSN 01384821

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Abstract
A vertextransitive map X is a map on a closed surface on which the automorphism group Aut (X) acts transitively on the set of vertices. If the facecycles at all the vertices in a map are of same type then the map is said to be a semiequivelar map. Clearly, a vertextransitive map is semiequivelar. Converse of this is not true in general. We show that there are eleven types of semiequivelar maps on the torus. Three of these are equivelar maps. It is known that two of these three types are always vertextransitive. We show that this is true for the remaining one type of equivelar maps and one other type of semiequivelar maps, namely, if X is a semiequivelar map of type [ 6 3] or [ 3 3, 4 2] then X is vertextransitive. We also show, by presenting examples, that this result is not true for the remaining seven types of semiequivelar maps. There are ten types of semiequivelar maps on the Klein bottle. We present examples in each of the ten types which are not vertextransitive.
Item Type:  Journal Article 

Publication:  Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 
Publisher:  Springer Verlag 
Additional Information:  The copyright for this article belongs to the Authors. 
Keywords:  Archimedean tiling; Equivelar maps; Polyhedral map on torus; Vertextransitive map 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  29 May 2022 07:39 
Last Modified:  29 May 2022 07:39 
URI:  https://eprints.iisc.ac.in/id/eprint/72768 
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