{
  "id": "2007.02401",
  "version": "v1",
  "published": "2020-07-05T18:02:03.000Z",
  "updated": "2020-07-05T18:02:03.000Z",
  "title": "Graded Betti numbers of some circulant graphs",
  "authors": [
    "Sonica Anand",
    "Amit Roy"
  ],
  "comment": "20 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be the circulant graph $C_n(S)$ with $S \\subseteq \\{1, 2, \\dots, \\lfloor \\frac{n}{2} \\rfloor\\}$, and let $I(G)$ denote the edge ideal in the polynomial ring $R=\\mathbb{K}[x_0, x_1, \\dots, x_{n-1}]$ over a field $\\mathbb{K}$. In this paper, we compute the $\\mathbb{N}$-graded Betti numbers of the edge ideals of three families of circulant graphs $C_n(1,2,\\dots,\\widehat{j},\\dots,\\lfloor \\frac{n}{2} \\rfloor)$, $C_{lm}(1,2,\\dots,\\widehat{2l},\\dots, \\widehat{3l},\\dots,\\lfloor \\frac{lm}{2} \\rfloor)$ and $C_{lm}(1,2,\\dots,\\widehat{l},\\dots,\\widehat{2l},\\dots, \\widehat{3l},\\dots,\\lfloor \\frac{lm}{2} \\rfloor)$. Other algebraic and combinatorial properties like regularity, projective dimension, induced matching number and when such graphs are well-covered, Cohen-Macaulay, Sequentially Cohen-Macaulay, Buchsbaum and $S_2$ are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-05T18:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55",
      "13H10",
      "05C75",
      "05E45"
    ],
    "keywords": [
      "graded betti numbers",
      "circulant graph",
      "edge ideal",
      "cohen-macaulay",
      "combinatorial properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}