On the minimal energy ordering of trees with perfect matchings
The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of the graph. Zhang and Li [F. Zhang, H. Li, On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 7184] determined the first two smallest-energy trees of a fixed size with a perfect matching and showed that the third minimal energy is between two trees. This paper characterizes trees of a fixed size with a perfect matching with third minimal, fourth minimal and fifth minimal energies for n?86 n ? 86 and third minimal, fourth minimal energies for 14?n?84 14 ? n ? 84 .
energy tree perfect matching eigenvalues characteristic polynomial