Abstract and Applied Analysis

Some Properties on Estrada Index of Folded Hypercubes Networks

Jia-Bao Liu, Xiang-Feng Pan, and Jinde Cao

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Abstract

Let G be a simple graph with n vertices and let λ1,λ2,,λn be the eigenvalues of its adjacency matrix; the Estrada index EEG of the graph G is defined as the sum of the terms eλi,  i=1,2,,n. The n-dimensional folded hypercube networks FQn are an important and attractive variant of the n-dimensional hypercube networks Qn, which are obtained from Qn 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 FQn 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 FQn are proposed.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 167623, 6 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278601

Digital Object Identifier
doi:10.1155/2014/167623

Mathematical Reviews number (MathSciNet)
MR3166571

Zentralblatt MATH identifier
07021848

Citation

Liu, Jia-Bao; Pan, Xiang-Feng; Cao, Jinde. Some Properties on Estrada Index of Folded Hypercubes Networks. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 167623, 6 pages. doi:10.1155/2014/167623. https://projecteuclid.org/euclid.aaa/1412278601


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