Constructions of strongly regular Cayley graphs derived from weakly regular bent functions

Abstract

In this paper, inspired by the work of Tan et al. (2010) [36], Chee et al. (2011) [11] and Hyun et al. (2020) [19], we propose two new constructions of strongly regular graphs on finite fields by using weakly regular bent functions, which generalize the results in the existing references. We obtain two families of strongly regular graphs with flexible parameters. We are also able to obtain a 3-class amorphic association scheme. Moreover, we show that many of the strongly regular graphs which we construct are Ramanujan graphs.