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- W3100615995 abstract "A vertex-transitive map X is a map on a closed surface on which the automorphism group $$mathrm{Aut}(X)$$ acts transitively on the set of vertices. If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse of this is not true in general. We show that there are eleven types of semi-equivelar maps on the torus. Three of these are equivelar maps. It is known that two of these three types are always vertex-transitive. We show that this is true for the remaining one type of equivelar maps and one other type of semi-equivelar maps, namely, if X is a semi-equivelar map of type $$[6^3]$$ or $$[3^3, 4^2]$$ then X is vertex-transitive. We also show, by presenting examples, that this result is not true for the remaining seven types of semi-equivelar maps. There are ten types of semi-equivelar maps on the Klein bottle. We present examples in each of the ten types which are not vertex-transitive." @default.
- W3100615995 created "2020-11-23" @default.
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- W3100615995 date "2017-02-23" @default.
- W3100615995 modified "2023-10-14" @default.
- W3100615995 title "Semi-equivelar and vertex-transitive maps on the torus" @default.
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- W3100615995 doi "https://doi.org/10.1007/s13366-017-0332-z" @default.
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