A study on Type-2 isomorphic circulant graphs. Part 8: Isomorphism series, digraph and graph of C_n(R)

@misc{kamalappan2026study,
  title = {{A study on Type-2 isomorphic circulant graphs. Part 8: Isomorphism series, digraph and graph of $C_n(R)$}},
  author = {V. Vilfred Kamalappan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.20984},
  eprint = {2606.20984},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.20984},
  note = {CC BY-NC-SA 4.0},
}

TY  - UNPB
TI  - A study on Type-2 isomorphic circulant graphs. Part 8: Isomorphism series, digraph and graph of C_n(R)
AU  - V. Vilfred Kamalappan
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2606.20984
UR  - https://arxiv.org/abs/2606.20984
AB  - 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} 𝒟 and {\em isomorphism graph} 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.
ER  -