1. On the minimal energy of trees with a given diameter
- Author
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Yan, Weigen and Ye, Luzhen
- Subjects
- *
LEAST absolute deviations (Statistics) , *MOLECULES , *LEAST squares , *EIGENVALUES - Abstract
Abstract: The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. F. Zhang, H. Li [On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71–84] characterized the trees with a perfect matching having the minimal and the second minimal energies, which solved a conjecture proposed by I. Gutman [Acyclic conjugated molecules, trees and their energies, J. Math. Chem. 1 (1987) 123–143]. In this letter, for a given positive integer we characterize the tree with the minimal energy having diameter at least . As a corollary, we also characterize the tree with the minimal Hosoya index having diameter at least . [Copyright &y& Elsevier]
- Published
- 2005
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