{
  "id": "2308.06040",
  "version": "v1",
  "published": "2023-08-11T09:36:40.000Z",
  "updated": "2023-08-11T09:36:40.000Z",
  "title": "Algebraic connectivity of Kronecker products of line graphs",
  "authors": [
    "Shivani Chauhan",
    "A. Satyanarayana Reddy"
  ],
  "comment": "14 pages, accepted for publication in Discrete Mathematics, Algorithms and Applications",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $X$ be a tree with $n$ vertices and $L(X)$ be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of $L(X)\\times K_m$ is equal to $m-1$, where $\\times$ denotes the Kronecker product. We provide a few necessary and sufficient conditions for $L(X)\\times K_m$ to be Laplacian integral. The algebraic connectivity of $L(X)\\times K_m$, where $X$ is a tree of diameter $4$ and $k$-book graph is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T09:36:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C76"
    ],
    "keywords": [
      "algebraic connectivity",
      "kronecker product",
      "line graph",
      "book graph",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}