{
  "id": "0709.2217",
  "version": "v1",
  "published": "2007-09-14T07:24:12.000Z",
  "updated": "2007-09-14T07:24:12.000Z",
  "title": "A classification of prime-valent regular Cayley maps on some groups",
  "authors": [
    "Dongseok Kim",
    "Young Soo Kwon",
    "Jaeun Lee"
  ],
  "journal": "Bull. Korean Math. Soc. 47 (2010) 17-27",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are balanced and all prime-valent regular Cayley maps on abelian groups are either balanced or anti-balanced. Furthermore, we prove that there is no prime-valent regular Cayley map on any dicyclic group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-14T07:24:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C30"
    ],
    "keywords": [
      "prime-valent regular cayley map",
      "classification",
      "abelian groups",
      "dihedral groups",
      "dicyclic group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2217K"
    }
  }
}