{
  "abstract": "The extremal problem of determining the graphs with maximum spectral radius among all graphs with a prescribed number of edges was resolved by Rowlinson [Linear Algebra Appl. 110 (1988) 43--53]. A signed graph $Γ=(G,σ)$ is called $C_k^-$-free if it contains no negative $k$-cycle as a signed subgraph. The index of a signed graph is defined as the largest eigenvalue of its adjacency matrix. This paper addresses the maximization of the index of unbalanced signed graphs. For signed graphs of a prescribed order, Wang and Lin [Discrete Appl. Math. 372 (2025) 164--172] determined the maximum index of $C_4^{-}$-free unbalanced signed graphs. Subsequently, Wang, Peng and Hou [Discrete Math. 349 (2026) 114871] characterized the unbalanced signed graphs of prescribed size with maximum index. This paper treats the edge spectral Turán-type problem for $C_4^-$-free unbalanced signed graphs. The all-positive signed graph with underlying graph $G$ is denoted by $(G,+)$. Evidently, $A((G,+))=A(G)$. In particular, $(H_{d,t},+)$ is the all-positive signed graph whose underlying graph is $H_{d,t}$, where $H_{d,0}=K_d$ and for $t>0$, $H_{d,t}$ is obtained from $K_d$ by adding a single vertex adjacent to exactly $t$ vertices of $K_d$. Let $m-3=\\binom{d}{2}+t$ with $0\\le t\\le d-1$. Up to switching isomorphism and the addition of isolated vertices, the unique extremal unbalanced signed graph is obtained by attaching a negative triangle to a specified vertex of the all-positive signed graph $(H_{d,t},+)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30881",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhihui Yang"
    },
    {
      "name": "Dan Li"
    },
    {
      "name": "Yuanyuan Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4j1b7tr5185j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30881",
  "fulltext_url": null,
  "id": "e4j1b7tr5185j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30881",
  "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": "W7223335882",
  "pdf_url": "https://arxiv.org/pdf/2610.30881",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4j1b7tr5185j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30881",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30881"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the maximal index of $C_4^-$-free unbalanced signed graphs of prescribed size",
  "title_text": "On the maximal index of C_4^--free unbalanced signed graphs of prescribed size",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/e4j1b7tr5185j",
  "venue": "arXiv",
  "versions": []
}