{
  "id": "2110.12375",
  "version": "v4",
  "published": "2021-10-24T07:31:40.000Z",
  "updated": "2022-07-12T17:10:26.000Z",
  "title": "Semi-equivelar toroidal maps and their vertex covers",
  "authors": [
    "Arnab Kundu",
    "Dipendu Maity"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "If the face\\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\\mbox{-}equivelar. A map is called minimal if the number of vertices is minimal. We know the bounds of number of vertex orbits of semi-equivelar toroidal maps. These bounds are sharp. Datta \\cite{BD2020} has proved that every semi-equivelar toroidal map has a vertex-transitive cover. In this article, we prove that if a semi-equivelar map is $k$ orbital then it has a finite index $m$-orbital minimal cover for $m \\le k$. We also show the existence and classification of $n$-sheeted covers of semi-equivelar toroidal maps for each $n \\in \\mathbb{N}$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2022-07-12T17:10:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C20",
      "52B70",
      "51M20",
      "57M60"
    ],
    "keywords": [
      "semi-equivelar toroidal map",
      "vertex covers",
      "orbital minimal cover",
      "vertex orbits",
      "finite index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}