Unicyclic graphs with minimal energy

If G is a graph and lambda (1), lambda (2), . . ., lambda (n) are its eigen values, then the energy of G is defined as E(G) = \lambda (1)\ + \lambda (2 )\ +... + \lambda (n)\. Let S-n(3) be the graph obtained from the star grap h with n vertices by adding an edge. In this paper we prove that Sn3 is the unique minimal energy graph among all unicyclic graphs with n vertices (n greater than or equal to 6).