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On the minimal energy of trees with a given diameter
- Source :
-
Applied Mathematics Letters . Sep2005, Vol. 18 Issue 9, p1046-1052. 7p. - Publication Year :
- 2005
-
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]
- Subjects :
- *LEAST absolute deviations (Statistics)
*MOLECULES
*LEAST squares
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 08939659
- Volume :
- 18
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics Letters
- Publication Type :
- Academic Journal
- Accession number :
- 18027723
- Full Text :
- https://doi.org/10.1016/j.aml.2004.11.001