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

Abstract

A weighing matrix W is quasi-balanced if |W||W|⊤=|W|⊤|W| has at most two off-diagonal entries, where |W|ij=|Wij|. 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.