{
  "id": "1606.07258",
  "version": "v1",
  "published": "2016-06-23T10:20:34.000Z",
  "updated": "2016-06-23T10:20:34.000Z",
  "title": "On the power graph of the direct product of two groups",
  "authors": [
    "A. K. Bhuniya",
    "Sajal Kumar Mukherjee"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The power graph $P(G)$ of a finite group $G$ is the graph with vertex set $G$ and two distinct vertices are adjacent if either of them is a power of the other. Here we show that the power graph $P(G_1 \\times G_2)$ of the direct product of two groups $G_1$ and $G_2$ is not isomorphic to either of the direct, cartesian and normal product of their power graphs $P(G_1)$ and $P(G_2)$. A new product of graphs, namely generalized product, has been introduced and we prove that the power graph $P(G_1 \\times G_2)$ is isomorphic to a generalized product of $P(G_1)$ and $P(G_2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-23T10:20:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "power graph",
      "direct product",
      "generalized product",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}