{
  "id": "2501.03806",
  "version": "v1",
  "published": "2025-01-07T14:18:04.000Z",
  "updated": "2025-01-07T14:18:04.000Z",
  "title": "Bounds on $A_α$-eigenvalues using graph invariants",
  "authors": [
    "João Domingos Gomes da Silva Junior",
    "Carla Silva Oliveira",
    "Liliana Manuela Gaspar Cerveira da Costa"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 2017, Nikiforov introduced the concept of the $A_{\\alpha}$-matrix, as a linear convex combination of the adjacency matrix and the degree diagonal matrix of a graph. This matrix has attracted increasing attention in recent years, as it serves as a unifying structure that combines the adjacency matrix and the signless Laplacian matrix. In this paper, we present some bounds for the largest and smallest eigenvalue of $A_{\\alpha}$-matrix involving invariants associated to graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-07T14:18:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graph invariants",
      "adjacency matrix",
      "degree diagonal matrix",
      "linear convex combination",
      "signless laplacian matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}