A study on Type-2 isomorphic circulant graphs. PART 9: Computer programs to show Type-1 $\&$ -2 isomorphic circulant graphs

TL;DR

This paper presents computer programs that demonstrate and analyze Type-1 and Type-2 isomorphisms in circulant graphs, aiding in their identification and theoretical development.

Contribution

It introduces specific software tools, C++ and VB programs, for showing and verifying Type-1 and Type-2 isomorphic circulant graphs, facilitating further research.

Findings

Families of Type-2 isomorphic circulant graphs were obtained using the programs.

The programs help in checking and finding isomorphic circulant graphs of given orders.

Tools support the development of theory on Type-2 isomorphic circulant graphs.

Abstract

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}.