{
  "abstract": "Let $K_t$ be obtained by attaching a pendant path of length $t$ to a fixed rooted graph $K$. We prove that $\\mathrm{Mo}(L(K_t))-\\mathrm{Mo}(K_t)$, the difference between its line-graph and original Mostar indices, is exactly affine on each parity class beyond a sharp uniform cutoff. The slope depends on distance-level neighbor counts and is positive for every non-bipartite core. Triangle chains give infinitely many graphs with $\\mathrm{Mo}(L(G))>\\mathrm{Mo}(G)$ at every positive cyclomatic number $c$, with maximum degree three, resolving Alex-Indulal Problem 3.3. At zero slope, a cactus branch-mass formula decides equality; identical vertex profiles need not give identical intercepts. Fixed cores giving equality for all sufficiently long attachments exist exactly when $c$ is odd. Maximum degree three suffices, and at every even $c$ a binary-tree construction gives equality on one eventual parity class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00829",
  "author_total": 1,
  "authors": [
    {
      "name": "Kerem Kat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ep458qb7zg2z7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00829",
  "fulltext_url": null,
  "id": "ep458qb7zg2z7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00829",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7216462921",
  "pdf_url": "https://arxiv.org/pdf/2610.00829",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ep458qb7zg2z7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00829"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Reversing the Mostar line-graph inequality with long pendant paths",
  "title_text": "Reversing the Mostar line-graph inequality with long pendant paths",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ep458qb7zg2z7",
  "venue": "arXiv",
  "versions": []
}