{
  "annotation_id": "83c04dbb-5d93-480f-bdd7-efb7d0af54ec",
  "date_created": "2026-02-17T05:53:23.555000Z",
  "date_modified": "2026-02-17T05:53:23.555000Z",
  "file_hash": "915e54393753069530a9e26a695b5803ca134fed4bf90b9a40d92dfcaeeaeee3",
  "private": false,
  "record": {
    "abstract": "For a graph $G$, let $\\lambda_1(G)$ and $\\lambda_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $\\lambda_1(G) + \\lambda_2(G)$ is called the \\emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $\\alpha \\in [0,1]$, we determine the extremal trees which maximize the convex combination $\\alpha \\lambda_1 + (1-\\alpha)\\lambda_2$ in the class of $n$-vertex trees.",
    "arxiv_id": "2601.10036",
    "authors": [
      "Hitesh Kumar",
      "Bojan Mohar",
      "Shivaramakrishna Pragada",
      "Hanmeng Zhan"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Convex combination of first and second eigenvalues of trees",
    "url": "https://arxiv.org/abs/2601.10036",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ae460906-0b4d-45dd-96eb-2247a011b135",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}