{
  "id": "1305.3414",
  "version": "v1",
  "published": "2013-05-15T10:13:44.000Z",
  "updated": "2013-05-15T10:13:44.000Z",
  "title": "More on the skew-spectra of bipartite graphs and Cartesian products of graphs",
  "authors": [
    "Xiaolin Chen",
    "Xueliang Li",
    "Huishu Lian"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a graph $G$, let $G^\\sigma$ be an oriented graph of $G$ with the orientation $\\sigma$ and skew-adjacency matrix $S(G^\\sigma)$. Then the spectrum of $S(G^\\sigma)$ is called the skew-spectrum of $G^\\sigma$, denoted by $Sp_S(G^\\sigma)$. It is known that a graph $G$ is bipartite if and only if there is an orientation $\\sigma$ of $G$ such that $Sp_S(G^\\sigma)=iSp(G)$. In [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electron. J. Combin. 20(2013), #P19], Cui and Hou conjectured that such orientation of a bipartite graph is unique under switching-equivalence. In this paper, we prove that the conjecture is true. Moreover, we give an orientation of the Cartesian product of a bipartite graph and a graph, and then determine the skew-spectrum of the resulting oriented product graph, which generalizes Cui and Hou's result, and can be used to construct more oriented graphs with maximum skew energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-15T10:13:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C50",
      "05C90"
    ],
    "keywords": [
      "cartesian product",
      "bipartite graph",
      "skew-spectrum",
      "orientation",
      "oriented graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.3414C"
    }
  }
}