{
  "id": "2406.07821",
  "version": "v1",
  "published": "2024-06-12T02:39:55.000Z",
  "updated": "2024-06-12T02:39:55.000Z",
  "title": "Walks, infinite series and spectral radius of graphs",
  "authors": [
    "Wenqian Zhang"
  ],
  "comment": "13 pages,0 figures, normal article",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph G, the spectral radius \\r{ho}(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between \\r{ho}(G) and the walks of the subgraphs of G. Especially, if G contains a complete multi-partite graph as a spanning subgraph, we give a formula for \\r{ho}(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-12T02:39:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "spectral radius",
      "infinite series",
      "current popular spectral extremal problem",
      "complete multi-partite graph",
      "largest eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}