Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14140 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916011868946432 |
|---|---|
| author | Kamalappan, Vilfred Peraprakash, Wilson |
| author_facet | Kamalappan, Vilfred Peraprakash, Wilson |
| contents | 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. $m$ $\ni$ $m$ = $\gcd(n, r) > 1$, $r\in R$ and $r,n\in\mathbb{N}$ and studied such graphs for $m$ = 2 in \cite{v13,v20}. But obtaining Type-2 isomorphic circulant graphs is not easy. 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. $m$ = $p$ for $n\in\mathbb{N}$ and $p$ is an odd prime. 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 and is very useful to develop its theory on Type-2 isomorphic circulant graphs \cite{v2-1}-\cite{v2-10}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\&$ -2 isomorphic circulant graphs Kamalappan, Vilfred Peraprakash, Wilson Combinatorics 05C60, 05C25, 05C75 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. $m$ $\ni$ $m$ = $\gcd(n, r) > 1$, $r\in R$ and $r,n\in\mathbb{N}$ and studied such graphs for $m$ = 2 in \cite{v13,v20}. But obtaining Type-2 isomorphic circulant graphs is not easy. 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. $m$ = $p$ for $n\in\mathbb{N}$ and $p$ is an odd prime. 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 and is very useful to develop its theory on Type-2 isomorphic circulant graphs \cite{v2-1}-\cite{v2-10}. |
| title | A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\&$ -2 isomorphic circulant graphs |
| topic | Combinatorics 05C60, 05C25, 05C75 |
| url | https://arxiv.org/abs/2605.14140 |