{
  "id": "2211.05559",
  "version": "v1",
  "published": "2022-11-10T13:24:30.000Z",
  "updated": "2022-11-10T13:24:30.000Z",
  "title": "Greedy trees have minimum Sombor indices",
  "authors": [
    "Ivan Damnjanović",
    "Dragan Stevanović"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, Gutman [MATCH Commun. Math. Comput. Chem. 86 (2021) 11-16] defined a new graph invariant which is named the Sombor index $\\mathrm{SO}(G)$ of a graph $G$ and is computed via the expression \\[ \\mathrm{SO}(G) = \\sum_{u \\sim v} \\sqrt{\\mathrm{deg}(u)^2 + \\mathrm{deg}(v)^2} , \\] where $\\mathrm{deg}(u)$ represents the degree of the vertex $u$ in $G$ and the summing is performed across all the unordered pairs of adjacent vertices $u$ and $v$. Here we take into consideration the set of all the trees $\\mathcal{T}_D$ that have a specified degree sequence $D$ and show that the greedy tree attains the minimum Sombor index on the set $\\mathcal{T}_D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T13:24:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C09",
      "05C05",
      "05C07"
    ],
    "keywords": [
      "minimum sombor index",
      "greedy tree attains",
      "adjacent vertices",
      "graph invariant",
      "match commun"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}