On acyclic conjugated molecules with minimal energies Original Research Article

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. In [5] Gutman (J. Math. Chem. 1 (1987) 123–143) proposes two conjectures about the minimum of the energy of conjugated trees (trees with a perfect matching). This paper mathematically verifies the two conjectures. In addition, trees with the second and the third smallest energies are also discussed.