{
  "abstract": "Mandal and Mehatari (\\emph{Comp.\\ Appl.\\ Math.}, 2025) introduced the class $\\mathcal{C}$ of cographs generated by a finite creation sequence $(α_1,\\dots,α_m)$ of natural numbers, and derived the inertia, an extended eigenvalue-free interval, and the exact characteristic polynomial for the \\emph{adjacency} matrix of such graphs. In this note we develop the parallel theory for the \\emph{distance Laplacian} matrix $D^L(G)$ and \\emph{distance signless Laplacian} matrix $D^Q(G)$. It is shown that $(0,α_{\\min}) \\cup (n-α_{\\min}, n)$, $(0,n) \\ \\cup\\ (n,\\,n+α_{\\min}) \\ \\cup\\ (2n-α_{\\min},\\,2n)$, $\\big(2\\Tr_{\\min},\\ μ_{\\max}(D^Q(G))\\big)$ are the eigenvalue-free intervals of the Laplacian, distance Laplacian, and distance signless Laplacian matrices respectively for the said class of graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08599",
  "author_total": 2,
  "authors": [
    {
      "name": "Santanu Mandal"
    },
    {
      "name": "Pallabi Manna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4y87cpvhnw7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08599",
  "fulltext_url": null,
  "id": "e4y87cpvhnw7e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08599",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7221061039",
  "pdf_url": "https://arxiv.org/pdf/2610.08599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4y87cpvhnw7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Distance Laplacian and Distance Signless Laplacian Spectra of $\\mathcal{C}$-Graphs",
  "title_text": "The Distance Laplacian and Distance Signless Laplacian Spectra of 𝒞-Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/e4y87cpvhnw7e",
  "venue": "arXiv",
  "versions": []
}