A Characterization of Bent Functions in Terms of Strongly Regular Graphs

In this note we prove that bent functions can be precisely characterized in terms of a special class of strongly regular graphs, thus providing a positive answer to a question raised in the paper Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem. (After publication of the above paper by the rst two authors, the third sent them a remark showing that bent functions are exactly characterized by strongly regular graphs with the additional property e = d; from this exchange the present note originated.)