{
  "id": "1401.2741",
  "version": "v1",
  "published": "2014-01-13T08:09:18.000Z",
  "updated": "2014-01-13T08:09:18.000Z",
  "title": "Two-sided Cayley graphs",
  "authors": [
    "Moharram N. Iradmusa",
    "Cheryl E. Praeger"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We introduce a family of graphs that generalises the class of Cayley graphs. For non-empty subsets L, R of a group G, the two-sided Cayley graph 2SC(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if y=a^{-1}xb for some a in L and b in R. Thus, in common with Cayley graphs, two-sided Cayley graphs may be useful to model networks as the same routing and communication scheme can be implemented at each vertex. We determine when two-sided Cayley graphs are simple undirected graphs, and give sufficient conditions for them to be connected, vertex-transitive, or Cayley graphs. Several open problems are posed. Many examples are given, including one on 12 vertices with connected components of sizes 4 and 8.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-13T08:09:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "two-sided cayley graph 2sc",
      "non-empty subsets",
      "vertex set",
      "open problems",
      "model networks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2741I"
    }
  }
}