WEAKLY HADAMARD DIAGONALIZABLE GRAPHS

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.