{
  "id": "2004.09746",
  "version": "v1",
  "published": "2020-04-21T04:15:06.000Z",
  "updated": "2020-04-21T04:15:06.000Z",
  "title": "Normality of one-matching semi-Cayley graphs over finite abelian groups with maximum degree three",
  "authors": [
    "Majid Arezoomand",
    "Mohsen Ghasemi"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $\\Gamma$ is said to be a semi-Cayley graph over a group $G$ if it admits $G$ as a semiregular automorphism group with two orbits of equal size. We say that $\\Gamma$ is normal if $G$ is a normal subgroup of ${\\rm Aut}(\\Gamma)$. We prove that every connected intransitive one-matching semi-Cayley graph, with maximum degree three, over a finite abelian group is normal and characterize all such non-normal graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T04:15:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "finite abelian group",
      "maximum degree",
      "semiregular automorphism group",
      "normal subgroup",
      "non-normal graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}