{
  "abstract": "Elspas and Turner \\cite{eltu} raised a question on the isomorphism of $C_{16}(1,3,7)$ and $C_{16}(2,3,5)$ and Vilfred \\cite{v96} gave its answer by defining Type-2 isomorphism of $C_n(R)$ w.r.t. $m$ $\\ni$ $m$ = $\\gcd(n, r) > 1$ and also modified to $m$ and $m^3$ divides $\\gcd(n, r)$ and $n$, respectively, $r\\in R$ and $r,n\\in\\mathbb{N}$ and studied such graphs \\cite{v13,v20, v2-1}. Using a $C^{++}$ computer program, the authors obtained families of Type-2 isomorphic $C_{n}(R)$ w.r.t. $m$ = 2,3,5,7 for $n\\in\\mathbb{N}$ as well as $C_{np^3}(R)$ w.r.t. $m$ = $p$ where $p$ is a prime and $n\\in\\mathbb{N}$. In this paper, we present the $C^{++}$ program and also a VB program POLY415.EXE which is used to show how Type-1 and Type-2 isomorphisms of a circulant graph take place as well as for checking and finding Type-1 and Type-2 circulant graphs of a given order. This article is the $9^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \\cite{v2-1}-\\cite{v2-10}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.14140",
  "author_total": 2,
  "authors": [
    {
      "name": "Vilfred Kamalappan"
    },
    {
      "name": "Wilson Peraprakash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9m2k0b242575.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14140",
  "fulltext_url": null,
  "id": "a9m2k0b242575",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14140",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7161239190",
  "pdf_url": "https://arxiv.org/pdf/2605.14140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9m2k0b242575.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.14140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\\&$ -2 isomorphic circulant graphs",
  "title_text": "A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 & -2 isomorphic circulant graphs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/a9m2k0b242575",
  "venue": "arXiv",
  "versions": []
}