{
  "abstract": "This article is the $5^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \\cite{v2-1}-\\cite{v2-10} and is a continuation of Part 4. Here, we study Type-2 isomorphic circulant graphs of $C_{48}(r_1,r_2,r_3)$, $C_{81}(r_1,r_2,r_3)$ and $C_{96}(r_1,r_2,r_3,r_4)$. We find that for $n$ = 48,96, total number of pairs of isomorphic circulant graphs of Type-2 w.r.t. $m$ = 2 of the forms $C_{n}(r_1,r_2,r_3)$ and $C_{n}(s_1,s_2,s_3)$ are 18 and 72, respectively, and total number of triples of isomorphic circulant graphs of Type-2 w.r.t. $m$ = 3 of the form $C_{81}(x_1,x_2,x_3)$, $C_{81}(y_1,y_2,y_3)$ and $C_{81}(z_1,z_2,z_3)$ are 27.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12390",
  "author_total": 1,
  "authors": [
    {
      "name": "Vilfred Kamalappan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15ce6cz4dcq40.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12390",
  "fulltext_url": null,
  "id": "15ce6cz4dcq40",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12390",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7161060913",
  "pdf_url": "https://arxiv.org/pdf/2605.12390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15ce6cz4dcq40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.12390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96",
  "title_text": "A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/15ce6cz4dcq40",
  "venue": "arXiv",
  "versions": []
}