  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.
