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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.09384 |
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| _version_ | 1866913117796040704 |
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| author | Kamalappan, Vilfred |
| author_facet | Kamalappan, Vilfred |
| contents | This study is the $2^{nd}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Definition of Type-2 isomorphism of circulant graphs $C_n(R)$ w.r.t. $m$ was further modified by the author by considering $m > 1$ divides $\gcd(n, r)$, $m^3$ divides $n$ and $r\in R$ and studied Type-2 isomorphic circulant graphs w.r.t. $m$ = 2. This modification simplifies our calculations while finding isomorphic circulant graphs of Type-2. In this paper, using the modified definition \ref{d4.2}, we obtain Type-2 isomorphic circulant graphs of orders 16, 24 and 27 and show that the total number of pairs of Type-2 isomorphic circulant graphs of orders 16 and 24 are 8 and 32, respectively and the total number of triples of Type-2 isomorphic circulant graphs of order 27 are 12. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27 Kamalappan, Vilfred Combinatorics 05C60, 05C25, 05C75 This study is the $2^{nd}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Definition of Type-2 isomorphism of circulant graphs $C_n(R)$ w.r.t. $m$ was further modified by the author by considering $m > 1$ divides $\gcd(n, r)$, $m^3$ divides $n$ and $r\in R$ and studied Type-2 isomorphic circulant graphs w.r.t. $m$ = 2. This modification simplifies our calculations while finding isomorphic circulant graphs of Type-2. In this paper, using the modified definition \ref{d4.2}, we obtain Type-2 isomorphic circulant graphs of orders 16, 24 and 27 and show that the total number of pairs of Type-2 isomorphic circulant graphs of orders 16 and 24 are 8 and 32, respectively and the total number of triples of Type-2 isomorphic circulant graphs of order 27 are 12. |
| title | A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27 |
| topic | Combinatorics 05C60, 05C25, 05C75 |
| url | https://arxiv.org/abs/2508.09384 |