Two characterizations of the grid graphs

In this paper we give two characterizations of the $p times q$-grid graphs as co-edge-regular graphs with four distinct eigenvalues.

Maximality of Seidel matrices and switching roots of graphs

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 $arccos1/3$. 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.