{
  "id": "2202.12895",
  "version": "v1",
  "published": "2022-02-25T05:43:48.000Z",
  "updated": "2022-02-25T05:43:48.000Z",
  "title": "Application of Tikhonov Regularization in Generalized Inverse of Adjacency Matrix of Undirected Graph",
  "authors": [
    "Paul Ryan Longhas",
    "Alsafat Abdul"
  ],
  "comment": "6, articles",
  "doi": "10.14445/22315373/IJMTT-V68I2P501",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we found the Moore-Penrose generalized inverse of adjacency matrix of an undirected graph, explicitly. We proved that the matrix $R_\\lambda= [r_{ij}]$ is nonsingular where $r_{ii}=\\frac{1}{\\lambda}+ \\deg v_i$ and $r_{ij}=\\mid N_G(V_i)\\cap N_G(V_j)\\mid$ for $i\\neq j$, and we proved that $A^{\\dagger}_G=[s_{ij}]_{1\\leq i, j \\leq n}$ where $\\displaystyle{s_{ij}=s_{ji}=\\lim_{\\lambda \\rightarrow +\\infty} \\langle R^{-1}_{\\lambda}e_j, f_i \\rangle }$. The proof of the main result was based on the Tikhonov regularization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-25T05:43:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "tikhonov regularization",
      "adjacency matrix",
      "undirected graph",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}