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PreprintCC BY-NC-SA 4.0arXiv

A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups (T2n,m(Cn(R)), ∘) and (Vn,m(Cn(R)), ∘)

  • Vilfred Kamalappan
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Abstract

This article is the 6th part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. In this part, we define Vn,m(Cn(R)) and Type-2 set T2n,m(Cn(R)) of Cn(R) and present their properties. We prove that (Vn,m(Cn(R)), ∘) is an Abelian group and (T2n,m(Cn(R)), ∘) is a subgroup of (Vn,m(Cn(R)), ∘) where T2n,m(Cn(R)) = {Cn(R)} ∪ {Cn(S): Cn(S) is Typ-2 isomorphic to Cn(R) w.r.t. m } and (T2n,m(Cn(R)), ∘) is the Type-2 group of Cn(R) w.r.t. m. We also present many examples of Type-1 and Type-2 groups where T1n(Cn(R)) = {Cn(xR): x∈φn} is the Type-1 set of Cn(R) and (T1n(Cn(R)), ∘') is its Type-1 group.

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Cite

BibTeXRIS
BibTeX
@misc{kamalappan2026study,
  title = {{A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups $(T2_n,m(C_n(R)), \circ)$ and $(V_n,m(C_n(R)), \circ)$}},
  author = {Vilfred Kamalappan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.12868},
  eprint = {2605.12868},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.12868},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - A study on Type-2 isomorphic circulant graphs. Part 6: Abelian groups (T2_n,m(C_n(R)), ∘) and (V_n,m(C_n(R)), ∘)
AU  - Vilfred Kamalappan
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2605.12868
UR  - https://arxiv.org/abs/2605.12868
AB  - This article is the 6^th part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. In this part, we define V_n,m(C_n(R)) and Type-2 set T2_n,m(C_n(R)) of C_n(R) and present their properties. We prove that (V_n,m(C_n(R)), ∘) is an Abelian group and (T2_n,m(C_n(R)), ∘) is a subgroup of (V_n,m(C_n(R)), ∘) where T2_n,m(C_n(R)) = {C_n(R)} ∪ {C_n(S): C_n(S) is Typ-2 isomorphic to C_n(R) w.r.t. m } and (T2_n,m(C_n(R)), ∘) is the Type-2 group of C_n(R) w.r.t. m. We also present many examples of Type-1 and Type-2 groups where T1_n(C_n(R)) = {C_n(xR): x∈φ_n} is the Type-1 set of C_n(R) and (T1_n(C_n(R)), ∘') is its Type-1 group.
ER  -