English

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

Combinatorics 2026-05-13 v1

Abstract

This study is the 5th5^{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 C48(r1,r2,r3)C_{48}(r_1,r_2,r_3), C81(r1,r2,r3)C_{81}(r_1,r_2,r_3) and C96(r1,r2,r3,r4)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. mm = 2 of the forms Cn(r1,r2,r3)C_{n}(r_1,r_2,r_3) and Cn(s1,s2,s3)C_{n}(s_1,s_2,s_3) are 18 and 72 for nn = 48, 96, respectively and the total number of triples of isomorphic circulant graphs of Type-2 w.r.t. mm = 3 of the form C81(x1,x2,x3)C_{81}(x_1,x_2,x_3), C81(y1,y2,y3)C_{81}(y_1,y_2,y_3) and C81(z1,z2,z3)C_{81}(z_1,z_2,z_3) are 27.

Keywords

Cite

@article{arxiv.2605.12390,
  title  = {A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96},
  author = {Vilfred Kamalappan},
  journal= {arXiv preprint arXiv:2605.12390},
  year   = {2026}
}