Acyclic molecules with second maximal energy

The sum of the absolute values of all eigenvalues of A ( G ) , the adjacency matrix of graph G , is defined as the energy of G . Acyclic molecular graphs with second maximal energy are characterized in this work. They are all n -vertex trees obtained by pasting an endpoint of path P n − 4 to the middle vertex of P 5 if the order n ≥ 6 .