{
  "abstract": "Let $G=(V(G),E(G))$ be a finite connected simple graph. The edge-connectivity $λ(G)$ of $G$ is the minimum number of edges that must be removed to make $G$ disconnected. We call $G$ maximally edge-connected when $λ(G)=δ(G)$, where $δ(G)$ is the minimum degree of $G$. The square graph $G^2$ of $G$ is the graph with vertex set $V(G)$, where two distinct vertices $u$ and $v$ are adjacent in $G^2$ precisely when their distance in $G$ is at most two. In this paper, first we prove that if $λ(G)\\geq4$ and $λ(G^2)<δ(G^2)$, then $λ(G^2)>λ(G)^{3/2}-\\frac54λ(G)$, which extends the result in \\cite{ChenXu} from the edge-connectivity range $4\\leqλ(G)\\leq7$ to $λ(G)\\geq4$. Then we show that $G^2$ is maximally edge-connected if one of the following conditions hold: (i) $δ(G)\\geq\\lfloor(n+2)/4\\rfloor$, or $δ(G)\\leq\\lfloor(n+2)/4\\rfloor-1$ and $\\sum_{i=1}^{2k}d_{n+1-i}\\geq k(n-4)-2δ(G)+3$, where $k$ is an integer satisfying $2\\leq k\\leqδ(G)+2$ and $d_1\\geq d_2\\geq\\cdots\\geq d_n$ are the degrees of $G$; (ii) $d_{n-δ(G)}+d_n\\geq(3n-9)/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25386",
  "author_total": 2,
  "authors": [
    {
      "name": "Kai Li"
    },
    {
      "name": "Yingzhi Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xb65jt24pae1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25386",
  "fulltext_url": null,
  "id": "2xb65jt24pae1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25386",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223014483",
  "pdf_url": "https://arxiv.org/pdf/2610.25386",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xb65jt24pae1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25386",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25386"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the maximally edge-connected square graphs with degree sequence conditions",
  "title_text": "On the maximally edge-connected square graphs with degree sequence conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2xb65jt24pae1",
  "venue": "arXiv",
  "versions": []
}