Acyclic molecules with second maximal energy

The sum of the absolute values of all eigenvalues of A(G)A(G), the adjacency matrix of graph GG, is defined as the energy of GG. Acyclic molecular graphs with second maximal energy are characterized in this work. They are all nn-vertex trees obtained by pasting an endpoint of path Pn−4Pn−4 to the middle vertex of P5P5 if the order n≥6n≥6.