Abstract:
A matrix is called weakly Hadamard if its entries are from
{0, −1, 1} and its non-consecutive columns (with some ordering) are orthogo nal. Unlike Hadamard matrices, there is a weakly Hadamard matrix of order
n for every n ≥ 1. In this work, graphs for which their Laplacian matrices
can be diagonalized by a weakly Hadamard matrix are studied. A number
of necessary and su cient conditions are veri ed along with identi cation of
numerous families of graphs whose Laplacian matrices can be diagonalized by
a weakly Hadamard matrix.
