On minimal energy ordering of acyclic conjugated molecules

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Gutman (Acyclic conjugated molecules, trees and their energies, J. Math. Chem. 1 (1987) 123-143) proposes two conjectures about the minimum of the energy of conjugated trees (trees with a perfect matching), which are verified by Zhang and Li (On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71-84). This paper focuses on the trees of conjugated hydrocarbons and gives roughly the first n/2 trees in the class in the increasing order of their energies.