2-uniform covers of $2$-semiequivelar toroidal maps

Dipendu Maity

2-uniform covers of $2$-semiequivelar toroidal maps

Combinatorics 2021-05-05 v1

Authors: Dipendu Maity

Abstract

If every vertex in a map has one out of two face-cycle types, then the map is said to be $2$ -semiequivelar. A 2-uniform tiling is an edge-to-edge tiling of regular polygons having $2$ distinct transitivity classes of vertices. Clearly, a $2$ -uniform map is $2$ -semiequivelar. The converse of this is not true in general. There are 20 distinct 2-uniform tilings (these are of $14$ different types) on the plane. In this article, we prove that a $2$ -semiequivelar toroidal map $K$ has a finite $2$ -uniform cover if the universal cover of $K$ is $2$ -uniform except of two types.

Keywords

2-semiequivelar maps 2-uniform tilings toroidal maps universal cover finite covers combinatorial maps graph theory

Cite

@article{arxiv.2105.01577,
  title  = {2-uniform covers of $2$-semiequivelar toroidal maps},
  author = {Dipendu Maity},
  journal= {arXiv preprint arXiv:2105.01577},
  year   = {2021}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2101.04373

2-uniform covers of $2$-semiequivelar toroidal maps

Abstract

Keywords

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