{
  "id": "2305.05878",
  "version": "v1",
  "published": "2023-05-10T03:52:04.000Z",
  "updated": "2023-05-10T03:52:04.000Z",
  "title": "On Zagreb indices of graphs",
  "authors": [
    "Batmend Horoldagva",
    "Kinkar Chandra Das"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let ${\\mathcal G}_n$ be the set of class of graphs of order $n$. The first Zagreb index $M_1(G)$ is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index $M_2(G)$ is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph $G$. The three set of graphs are as follows: \\begin{eqnarray*} &&A=\\left\\{G\\in {\\mathcal G}_n:\\,\\frac{M_1(G)}{n}>\\frac{M_2(G)}{m}\\right\\},~B=\\left\\{G\\in {\\mathcal G}_n:\\,\\frac{M_1(G)}{n}=\\frac{M_2(G)}{m}\\right\\} \\mbox{ and }&& &&~~~~~~~~~~~~~~~~~~~~~~~~~C=\\left\\{G\\in {\\mathcal G}_n:\\,\\frac{M_1(G)}{n}<\\frac{M_2(G)}{m}\\right\\}. \\end{eqnarray*} In this paper we prove that $|A|+|B|<|C|$. Finally, we give a conjecture $|A|<|B|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T03:52:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C07",
      "05C35",
      "05C90"
    ],
    "keywords": [
      "first zagreb index",
      "second zagreb index",
      "molecular graph",
      "adjacent vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}