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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 167623, 6 pages
http://dx.doi.org/10.1155/2014/167623
Research Article

Some Properties on Estrada Index of Folded Hypercubes Networks

1School of Mathematics Science, Anhui University, Hefei 230601, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Anhui Xinhua University, Hefei 230088, China
4Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 24 November 2013; Accepted 19 December 2013; Published 5 February 2014

Academic Editor: Qiankun Song

Copyright © 2014 Jia-Bao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a simple graph with vertices and let be the eigenvalues of its adjacency matrix; the Estrada index of the graph is defined as the sum of the terms ,   . The -dimensional folded hypercube networks are an important and attractive variant of the -dimensional hypercube networks , which are obtained from by adding an edge between any pair of vertices complementary edges. In this paper, we establish the explicit formulae for calculating the Estrada index of the folded hypercubes networks by deducing the characteristic polynomial of the adjacency matrix in spectral graph theory. Moreover, some lower and upper bounds for the Estrada index of the folded hypercubes networks are proposed.