Constructions of Strongly Regular Cayley Graphs Using Index Four Gauss Sums

TL;DR

This paper presents a novel method for constructing strongly regular Cayley graphs over finite fields using cyclotomic classes and index 4 Gauss sums, resulting in new graph families with unique parameters.

Contribution

It introduces a new construction technique for strongly regular Cayley graphs based on index 4 Gauss sums and cyclotomic classes, expanding known graph families.

Findings

Two infinite families of strongly regular graphs with new parameters

Construction method using union of cyclotomic classes and index 4 Gauss sums

Graphs exhibit strongly regular properties with specific parameters

Abstract

We give a construction of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.