A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27

Vilfred Kamalappan

A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27

Combinatorics 2026-05-13 v2

Authors: Vilfred Kamalappan

Abstract

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.

Keywords

circulant graphs Type-2 isomorphism graph theory isomorphic graphs

Cite

@article{arxiv.2508.09384,
  title  = {A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27},
  author = {Vilfred Kamalappan},
  journal= {arXiv preprint arXiv:2508.09384},
  year   = {2026}
}

Comments

This article is an extension and modified article of its previous version

A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27

Abstract

Keywords

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