{
  "abstract": "Let $G$ be a connected graph, and let $λ_1(G) > λ_2(G)$ denote its two largest adjacency eigenvalues. The spectral gap of $G$ is defined as the difference $λ_1(G) - λ_2(G)$. For integers $r\\geq 2$ and $s\\geq 0$, the double kite $DK(r,s)$ is formed by taking two vertex-disjoint copies of the complete graph $K_r$ and joining one specified vertex of each clique to a path with $s$ internal vertices. Stanić (2013) conjectured that every connected $n$-vertex graph with minimum adjacency spectral gap is a double kite. In this paper, we confirm this conjecture for sufficiently large $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37774",
  "author_total": 3,
  "authors": [
    {
      "name": "Lele Liu"
    },
    {
      "name": "Michael Tait"
    },
    {
      "name": "Yi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/712akhp9qcq68.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37774",
  "fulltext_url": null,
  "id": "712akhp9qcq68",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37774",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214944592",
  "pdf_url": "https://arxiv.org/pdf/2609.37774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/712akhp9qcq68.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Connected graphs with minimum adjacency spectral gap",
  "title_text": "Connected graphs with minimum adjacency spectral gap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/712akhp9qcq68",
  "venue": "arXiv",
  "versions": []
}