Strongly Regular Graphs From Unions of Cyclotomic Classes

TL;DR

This paper presents two novel methods for constructing strongly regular graphs using unions of cyclotomic classes and index 2 Gauss sums, resulting in twelve new infinite families with unique parameters.

Contribution

It introduces two new constructions of strongly regular Cayley graphs over finite fields based on cyclotomic classes and Gauss sums, expanding known graph families.

Findings

Twelve infinite families of strongly regular graphs with new parameters

Construction methods based on cyclotomic classes and Gauss sums

Graphs exhibit strongly regular properties with specific algebraic structures

Abstract

We give two constructions of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new parameters.