All primitive strongly regular graphs except four are hyperenergetic

The energy of a graph G , denoted by E ( G ) , is the sum of the absolute values of the eigenvalues of G . If G is a graph on n vertices and E ( G ) > 2 ( n − 1 ) , then G is called a hyperenergetic graph. In this paper, we prove that all primitive strongly regular graphs except s r g ( 5 , 2 , 0 , 1 ) , s r g ( 9 , 4 , 1 , 2 ) , s r g ( 10 , 3 , 0 , 1 ) , and s r g ( 16 , 5 , 0 , 2 ) are hyperenergetic.