A Study on Type-2 Isomorphic Circulant Graphs: Part 8: $C_{432}(R)$, $C_{6750}(S)$ -- each has 2 types of Type-2 isomorphic circulant graphs

TL;DR

This paper identifies two families of circulant graphs with multiple Type-2 isomorphic variants relative to different values of m, expanding understanding of their structural properties.

Contribution

It introduces two new families of circulant graphs exhibiting multiple Type-2 isomorphic forms for different m values, advancing the classification of such graphs.

Findings

Family of $C_{432}(R)$ has isomorphic graphs for m=2 and m=3.

Family of $C_{6750}(S)$ has isomorphic graphs for m=3 and m=5.

Part of a larger 10-part series on Type-2 isomorphic circulant graphs.

Abstract

In this study, we obtain the following two families of circulant graphs each has Type-2 isomorphic circulant graphs w.r.t. $m$ such that $m$ has more than one value. (i) Family of circulant graphs $C_{432}(R)$, each has isomorphic circulant graphs of Type-2 w.r.t. $m$ = 2 as well as $m$ = 3; and (ii) Family of circulant graphs $C_{6750}(S)$, each has isomorphic circulant graphs of Type-2 w.r.t. $m$ = 3 as well as $m$ = 5. This study is the $8^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}.