{
  "id": "2112.08085",
  "version": "v2",
  "published": "2021-12-15T12:41:20.000Z",
  "updated": "2022-06-22T10:52:10.000Z",
  "title": "HS-integral and Eisenstein integral mixed circulant graphs",
  "authors": [
    "Monu Kadyan",
    "Bikash Bhattacharjya"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2106.01261",
  "categories": [
    "math.CO"
  ],
  "abstract": "A mixed graph is called \\emph{second kind hermitian integral}(or \\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of second kind are integers. A mixed graph is called \\emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set $S$ for which a mixed circulant graph $\\text{Circ}(\\mathbb{Z}_n, S)$ is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, the eigenvalues and the HS-eigenvalues of some oriented circulant graphs are expressed in terms of generalized M$\\ddot{\\text{o}}$bius function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-22T10:52:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C25"
    ],
    "keywords": [
      "eisenstein integral mixed circulant graphs",
      "hs-integral",
      "eigenvalues",
      "kind hermitian integral",
      "mixed graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}