Construction of strongly regular Cayley graphs based on three-valued Gauss periods

TL;DR

This paper presents a new method for constructing strongly regular Cayley graphs using three-valued Gauss periods, leading to multiple new infinite families and sporadic examples, expanding the known classes of such graphs.

Contribution

It introduces a novel construction technique for strongly regular Cayley graphs based on three-valued Gauss periods, generalizing previous methods.

Findings

Two infinite families of strongly regular Cayley graphs were constructed.

One sporadic example of a strongly regular Cayley graph was identified.

The construction generalizes previous approaches in the literature.

Abstract

In this paper, we give a construction of strongly regular Cayley graphs on the additive groups of finite fields based on three-valued Gauss periods. As consequences, we obtain two infinite families and one sporadic example of new strongly regular Cayley graphs. This construction can be viewed as a generalization of that of strongly regular Cayley graphs obtained in \cite{BLMX}.