论文信息 - On the minimal energy of trees with a given diameter

On the minimal energy of trees with a given diameter

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 d we characterize the tree with the minimal energy having diameter at least d . As a corollary, we also characterize the tree with the minimal Hosoya index having diameter at least d .

Weigen Yan | Luzhen Ye | Weigen Yan | Luzhen Ye

[1] John L. Goldwasser,et al. Permanent of the Laplacian matrix of trees and bipartite graphs , 1984, Discret. Math..

[2] Lusheng Wang,et al. Hexagonal chains with minimal total π-electron energy , 2001 .

[3] Yaoping Hou,et al. Unicyclic graphs with maximal energy , 2002 .

[4] I. Gutman,et al. Mathematical Concepts in Organic Chemistry , 1986 .

[5] Yaoping Hou,et al. Bicyclic graphs with minimum energy , 2001 .

[6] I. Outman,et al. Acyclic conjugated molecules, trees and their energies , 1987 .

[7] Huaien Li. On minimal energy ordering of acyclic conjugated molecules , 1999 .

[8] Michael Doob,et al. Spectra of graphs , 1980 .

[9] Yaoping Hou,et al. Unicyclic Graphs with Minimal Energy , 2001 .

[10] Ivan Gutman,et al. Acyclic systems with extremal Hückel π-electron energy , 1977 .

[11] Lusheng Wang,et al. Hexagonal chains with maximal total π-electron energy , 2001 .

[12] Juan Rada,et al. Polygonal chains with minimal energy , 2003 .

[13] R. Balakrishnan. The energy of a graph , 2004 .

[14] Fuji Zhang,et al. On Acyclic Conjugated Molecules with Minimal Energies , 1999, Discret. Appl. Math..