Resolvent Estrada index of cycles and paths
Authors: Deng Bo, Wang Shouzhong, Gutman Ivan
Keywords: Resolvent Estrada index; Estrada index; spectrum (of graph); cycle; path
Abstract:
Let G be a simple graph of order n. The resolvent Estrada index of G is defined as EEr = nΣi=1 (1- λi/(n-1)^-1, where λ1;λ2;…;λn are the eigenvalues of G. Formulas for computing EEr of the cycle Cn and the path Pn are derived. The precision of these approximations are shown to be excellent. We also examine the difference and relations between the Estrada index and the resolvent Estrada index of Cn and Pn.
References:
[1] Benzi, M., Boito, P. (2010) Quadrature rule-based bounds for functions of adjacency matrices. Linear Algebra and its Applications, 433(3): 637-652
[2] Chen, X., Qian, J. (2012) Bounding the resolvent Estrada index of a graph. J. Math. Study, Vol. 45, 2, 159-166
[3] Chen, X., Qian, J. (2015) On resolvent Estrada index. MATCH Commun. Math. Comput. Chem, Vol. 73, 1, 163-174
[4] Cvetković, D.M., Doob, M., Sachs, H. (1980) Spectra of graphs: Theory and application. New York: Academic Press
[5] de la Pena, J.A., Gutman, I., Rada, J. (2007) Estimating the Estrada index. Linear Algebra and its Applications, 427(1): 70-76
[6] Deng, H. (2009) A note on the Estrada index of trees. Match Commun. Math. Comput. Chem, 62(3): 607
[7] Estrada, E. (2000) Characterization of 3D molecular structure. Chemical Physics Letters, 319(5-6), 713-718
[8] Estrada, E. (2002) Characterization of the folding degree of proteins. Bioinformatics (Oxford, England), 18(5): 697-704
[9] Estrada, E., Higham, D.J. (2010) Network Properties Revealed through Matrix Functions. SIAM Review, 52(4): 696-714
[10] Estrada, E., Rodríguez-Velázquez, J. (2005) Subgraph centrality in complex networks. Physical Review E, 71(5): 056103-1-9
[11] Gutman, I., Deng, H., Radenković, S. (2011) The Estrada index: An updated survey. u: Cvetković D., Gutman I. [ur.] Selected topics on applications of graph spectra, Belgrade: Math. Inst, pp. 155-174
[12] Gutman, I., Furtula, B., Chen, X., Qian, J. (2015) Graphs with smallest resolvent Estrada indices. MATCH Commun. Math. Comput. Chem, Vol. 73, 1, 267-270
[13] Gutman, I., Furtula, B., Chen, X., Qian, J. (2015) Resolvent Estrada index – computational and math- ematical studies. MATCH Commun. Math. Comput. Chem, Vol. 74, 3, 431-440
[14] Gutman, I., Graovac, A. (2007) Estrada index of cycles and paths. Chemical Physics Letters, 436(1-3): 294-296