Ordering of Hückel trees according to minimal energies

The tree with a perfect matching having degrees not greater than three is referred to as the Hückel tree. The ordering of Hückel trees according to their minimal energies is investigated by means of a quasi-ordering relation. Using a simpler method than that of Li [H. Li, On minimal energy ordering of acyclic conjugated molecules, J. Math. Chem. 25 (1999) 145–169], we obtain the first 2n-10-[(1+(-1)n]/2 trees in the increasing order of their energies within the class under consideration for n⩾13, where 2n is the vertex number of the tree. The number of the trees obtained here exceeds the reported result (Li, 1999) by n-10. We also get a lot of preceding trees in the increasing order of their energies within the class for 5⩽n⩽12.