# Codes and Expansions (CodEx) Seminar

## Steve Butler (Iowa State University)Hadamard diagonalizable graphs of small order

A graph is said to be Hadamard diagonalizable if there exists a Hadamard matrix which can diagonalize its Laplacian (or adjacency) matrix; equivalently there exists an orthonormal set of eigenvectors associated with the graph where each eigenvector has entries in $\pm1$. We establish some basic results including how using a combination of computation and theory has allowed us to determine all Hadamard diagonalizable graphs of order at most 36.

Joint work with Jane Breen, Melissa Fuentes, Bernard Lidický, Michael Phillips, Alex Riasanovsky, Sung-Yell Song, Ralihe Villagrán, Cedar Wiseman, and Xiaohong Zhang