A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96

TL;DR

This paper analyzes Type-2 isomorphic circulant graphs of specific orders, identifying counts of isomorphic pairs and triples, extending previous detailed studies on this graph class.

Contribution

It provides new counts of isomorphic circulant graph pairs and triples for orders 48, 81, and 96, advancing understanding of their structural properties.

Findings

18 pairs of isomorphic graphs for order 48

72 pairs of isomorphic graphs for order 96

27 triples of isomorphic graphs for order 81

Abstract

This study is the $5^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 4. Here, we study Type-2 isomorphic circulant graphs of $C_{48}(r_1,r_2,r_3)$, $C_{81}(r_1,r_2,r_3)$ and $C_{96}(r_1,r_2,r_3,r_4)$. We find that the total number of pairs of isomorphic circulant graphs of Type-2 w.r.t. $m$ = 2 of the forms $C_{n}(r_1,r_2,r_3)$ and $C_{n}(s_1,s_2,s_3)$ are 18 and 72 for $n$ = 48, 96, respectively and the total number of triples of isomorphic circulant graphs of Type-2 w.r.t. $m$ = 3 of the form $C_{81}(x_1,x_2,x_3)$, $C_{81}(y_1,y_2,y_3)$ and $C_{81}(z_1,z_2,z_3)$ are 27.