Quasi-balanced weighing matrices, signed strongly regular graphs and association schemes

Abstract

A weighing matrix $W$ is quasi-balanced if $|W||W{|}^{\top }=|W{|}^{\top }|W|$ has at most two off-diagonal entries, where $|W{|}_{ij}=|W_{ij}|$. A quasi-balanced weighing matrix $W$ signs a strongly regular graph if $|W|$ coincides with its adjacency matrix. Among other things, signed strongly regular graphs and their equivalent association schemes are presented.

25 pages