On acyclic conjugated molecules with minimal energies
Discrete Applied Mathematics
Trees with minimal Laplacian coefficients
Computers & Mathematics with Applications
Distance spectral radius of trees with given matching number
Discrete Applied Mathematics
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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) 71-84] 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 and third minimal, fourth minimal energies for 14@?n@?84.