Maximality of Seidel matrices and switching roots of graphs

Abstract

In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue 3, which gives a classification of maximal equiangular lines in a Euclidean space with angle arccos 1/3. Motivated by the maximality of the exceptional root system E 8 , we define strong maximality of a Seidel matrix, and show that every Seidel matrix achieving the absolute bound is strongly maximal.