{
  "id": "2505.05999",
  "version": "v1",
  "published": "2025-05-09T12:31:46.000Z",
  "updated": "2025-05-09T12:31:46.000Z",
  "title": "Edge-vertex degree based Zagreb index and graph operations",
  "authors": [
    "Amitariddhi Sinha",
    "Somnath Paul"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ consists of two parts, the vertices and edges. The vertices constitute the vertex set $V(G)$ and the edges, the edge set. An edge \\( e=xy \\), \\( ev \\)-dominates not only the vertices incident to it but also those adjacent to either \\( x \\) or \\( y \\). The edge-vertex degree of $e,$ $deg^{ev}_{G}(e),$ is the number of vertices in the $ev$-dominating set of $e$. In this article, we compute expressions for the $ev$-degree version of the Zagreb index of several unary and binary graph operations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T12:31:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C09",
      "05C76"
    ],
    "keywords": [
      "zagreb index",
      "edge-vertex degree",
      "binary graph operations",
      "vertex set",
      "vertices constitute"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}