{
  "id": "2406.03561",
  "version": "v1",
  "published": "2024-06-05T18:17:29.000Z",
  "updated": "2024-06-05T18:17:29.000Z",
  "title": "Energy of a graph and Randić index of subgraphs",
  "authors": [
    "Gerardo Arizmendi",
    "Diego Huerta"
  ],
  "comment": "12 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a new inequality between the energy of a graph and a weighted sum over the edges of the graph. Using this inequality we prove that $\\mathcal{E}(G)\\geq 2R(H)$, where $ \\mathcal{E}(G)$ is the energy of a graph $G$ and $R(H)$ is the Randi\\'c index of any subgraph of $G$ (not necessarily induced). In particular, this generalizes well-known inequalities $\\mathcal{E}(G)\\geq 2R(G)$ and $\\mathcal{E}(G)\\geq 2\\mu(G)$ where $\\mu(G)$ is the matching number. We give other inequalities as applications to this result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T18:17:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C09"
    ],
    "keywords": [
      "inequality",
      "generalizes well-known inequalities",
      "randic index",
      "weighted sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}