Strongly Regular Graphs Constructed from $p$-ary Bent Functions

TL;DR

This paper extends the construction of strongly regular graphs from ternary to p-ary bent functions, producing new graphs with diverse parameters and demonstrating the potential for novel graph structures.

Contribution

It generalizes previous methods to p-ary bent functions, enabling the creation of new strongly regular graphs with varied parameters.

Findings

Constructed strongly regular graphs from p-ary bent functions

Generated new graphs with small parameters using non-quadratic functions

Expanded the class of strongly regular graphs beyond previous ternary cases

Abstract

In this paper, we generalize the construction of strongly regular graphs in [Y. Tan et al., Strongly regular graphs associated with ternary bent functions, J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to $p$-ary bent functions, where $p$ is an odd prime. We obtain strongly regular graphs with three types of parameters. Using certain non-quadratic $p$-ary bent functions, our constructions can give rise to new strongly regular graphs for small parameters.