On acyclic conjugated molecules with minimal energies (Q1283072)

The energy of a graph is defined as the sum of the absolute values of all its eigenvalues and \textit{I. Gutman} [J. Math. Chem. 1, 123-144 (1987)] proposed two conjectures about the minimum energy of conjugated trees (trees with perfect matchings). The authors prove these conjectures and they also obtain some results on trees with the second and the third smallest energies.