Spectra and the exact number of Automorphisms of Paley-type graphs of order a product of n distinct primes

TL;DR

This paper extends the study of Paley-type graphs to orders that are products of multiple Pythagorean primes, determining their spectra and automorphism counts, thus broadening understanding of their algebraic and spectral properties.

Contribution

It introduces a generalization of Paley-type graphs to multiple Pythagorean primes and computes their spectra and automorphism groups, which was not previously known.

Findings

Determined the adjacency spectra of the generalized Paley-type graphs.

Calculated the exact number of automorphisms for these graphs.

Extended the class of known Paley-type graphs to products of multiple primes.

Abstract

Paley graphs are Cayley graphs which are circulant and strongly regular. Paley-type graph of order a product of two distinct Pythagorean primes was introduced by Dr Angsuman Das. In this paper, we extend the study of Paley-type graphs to the order a product of n distinct Pythagorean primes. We have determined its adjacency spectra and the exact number of the automorphisms.