{
  "id": "2309.12682",
  "version": "v1",
  "published": "2023-09-22T07:38:51.000Z",
  "updated": "2023-09-22T07:38:51.000Z",
  "title": "The comparison of two Zagreb-Fermat eccentricity indices",
  "authors": [
    "Xiangrui Pan",
    "Longyu Li",
    "Gengji Li",
    "Cheng Zeng"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we focus on comparing the first and second Zagreb-Fermat eccentricity indices of graphs. We show that $$\\frac{\\sum_{uv\\in E\\left( G \\right)}{\\varepsilon _3\\left( u \\right) \\varepsilon _3\\left( v \\right)}}{m\\left( G \\right)} \\leq \\frac{\\sum_{u\\in V\\left( G \\right)}{\\varepsilon _{3}^{2}\\left( u \\right)}}{n\\left( G \\right)} $$ holds for all acyclic and unicyclic graphs. Besides, we verify that the inequality may not be applied to graphs with at least two cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-22T07:38:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "comparison",
      "second zagreb-fermat eccentricity indices",
      "unicyclic graphs",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}