{
  "id": "math/0601361",
  "version": "v1",
  "published": "2006-01-14T20:02:22.000Z",
  "updated": "2006-01-14T20:02:22.000Z",
  "title": "The distinguishing number of the augmented cube and hypercube powers",
  "authors": [
    "Melody Chan"
  ],
  "comment": "10 pages, 1 figure, submitted to Discrete Mathematics",
  "categories": [
    "math.CO"
  ],
  "abstract": "The distinguishing number of a graph G, denoted D(G), is the minimum number of colors such that there exists a coloring of the vertices of G where no nontrivial graph automorphism is color-preserving. In this paper, we show that the distinguishing number of p-th graph power of the n-dimensional hypercube is 2 whenever 2 < p < n-1. This completes the study of the distinguishing number of hypercube powers. We also compute the distinguishing number of the augmented cube, a variant of the hypercube, answering an open question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-14T20:02:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C15"
    ],
    "keywords": [
      "distinguishing number",
      "hypercube powers",
      "augmented cube",
      "nontrivial graph automorphism",
      "p-th graph power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1361C"
    }
  }
}