English

On enumeration of a class of maps on Klein bottle

Combinatorics 2017-02-03 v2 Geometric Topology

Abstract

We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of the types {36}\{3^{6}\}, {44}\{4^{4}\}, {63}\{6^{3}\}, {33,\{3^{3}, 42}4^{2}\}, {32,\{3^{2}, 4,4, 3,3, 4}4\}, {3,\{3, 6,6, 3,3, 6}6\}, {34,6}\{3^{4}, 6\}, {4,\{4, 82}8^{2}\}, {3,122}\{3, 12^{2}\}, {4,\{4, 6,6, 12}12\}, {3,\{3, 4,4, 6,6, 4}4\}. In this article, we attempt to classify these maps.

Keywords

Cite

@article{arxiv.1509.04519,
  title  = {On enumeration of a class of maps on Klein bottle},
  author = {Dipendu Maity and Ashish Kumar Upadhyay},
  journal= {arXiv preprint arXiv:1509.04519},
  year   = {2017}
}