Graph spectra and the graph energy

There are several natural matrices that can be associated with a graph. The best-known instance is probably the adjacency matrix A(G) of a graph G. Fix an order of the vertices of G as v1, v2, . . . , vn. The entries aij of A(G) are defined as follows:

aij =

{ 1 if vi and vj are adjacent,

0 otherwise.