{
  "abstract": "This article is the $8^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \\cite{v2-1}-\\cite{v2-10}. In this study, we define {\\em isomorphic set}, {\\em isomorphism series}, {\\em isomorphism digraph} or {\\em isomorphism diagram} $\\mathcal{D}$ and {\\em isomorphism graph} $\\mathcal{G}$ of circulant graphs and obtain these corresponding to $C_{16}(R)$, $C_{27}(S)$ and $C_{54}(1,3,17,19)$ and present the isomorphism digraph and the isomorphism graph of $C_{432}(T)$ which has isomorphic circulant graphs of Type-2 w.r.t. $m$ = 2,3 and of $C_{6750}(U)$ which has isomorphic circulant graphs of Type-2 w.r.t. $m$ = 3,5 where $T$ = $\\{16, 27, 48, 54, 128, 160, 189\\}$ and $U$ = $\\{135, 243, 250, 750, 1107, 1593, 2000, 2457, 2500, 2943\\}$. We also define {\\em diameter of isomorphic set} of $C_n(R)$ and {\\em isomorphic distance} between any two circulant graphs. We find that the order of isomorphic sets of $C_{432}(T)$ and $C_{6750}(U)$ are 36 and 450 and their diameters are 3 and 3, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.20984",
  "author_total": 1,
  "authors": [
    {
      "name": "V. Vilfred Kamalappan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gzbvy803mx8n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.20984",
  "fulltext_url": null,
  "id": "2gzbvy803mx8n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.20984",
  "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": "W7165664604",
  "pdf_url": "https://arxiv.org/pdf/2606.20984",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gzbvy803mx8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.20984",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.20984"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A study on Type-2 isomorphic circulant graphs. Part 8: Isomorphism series, digraph and graph of $C_n(R)$",
  "title_text": "A study on Type-2 isomorphic circulant graphs. Part 8: Isomorphism series, digraph and graph of C_n(R)",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2gzbvy803mx8n",
  "venue": "arXiv",
  "versions": []
}