论文信息 - Lower bounds for Estrada index and Laplacian Estrada index

Lower bounds for Estrada index and Laplacian Estrada index

Abstract Let G be an n -vertex graph. If λ 1 , λ 2 , … , λ n and μ 1 , μ 2 , … , μ n are the ordinary (adjacency) eigenvalues and the Laplacian eigenvalues of G , respectively, then the Estrada index and the Laplacian Estrada index of G are defined as EE ( G ) = ∑ i = 1 n e λ i and LEE ( G ) = ∑ i = 1 n e μ i , respectively. Some new lower bounds for EE and LEE are obtained and shown to be the best possible.

[1] I. Gutman,et al. More on the Laplacian Estrada index , 2009 .

[2] Ali Reza Ashrafi,et al. Note on Estrada and $L$-Estrada indices of graphs , 2009 .

[3] Ernesto Estrada. Characterization of 3D molecular structure , 2000 .

[4] Ernesto Estrada,et al. Statistical-mechanical approach to subgraph centrality in complex networks , 2007, 0905.4098.

[5] J. A. Rodríguez-Velázquez,et al. Atomic branching in molecules , 2006 .

[6] A. Chang,et al. On the Laplacian Estrada index of a graph , 2009 .

[7] Gordon F. Royle,et al. Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[8] D. Cvetkovic,et al. Spectra of Graphs: Theory and Applications , 1997 .

[9] Anton Betten,et al. Algebraic Combinatorics and Applications : Proceedings , 2001 .

[10] Mar ´ ia Robbiano,et al. THE ENERGY AND AN APPROXIMATION TO ESTRADA INDEX OF SOME TREES , 2009 .

[11] J. A. Rodríguez-Velázquez,et al. Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12] B. Mohar. THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[13] I. Gutman. The Energy of a Graph: Old and New Results , 2001 .

[14] I. Gutman,et al. Laplacian energy of a graph , 2006 .

[15] M. Dehmer,et al. Analysis of Complex Networks: From Biology to Linguistics , 2009 .

[16] Ernesto Estrada. Spectral theory of networks : from biomolecular to ecological systems , 2009 .