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ESTRADA INDEX OF GENERAL WEIGHTED GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  28 September 2012

YILUN SHANG
YILUN SHANG*
Affiliation:
Institute for Cyber Security, University of Texas at San Antonio, San Antonio, Texas 78249, USA (email: shylmath@hotmail.com)
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Abstract

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Let $G$ be a general weighted graph (with possible self-loops) on $n$ vertices and $\lambda _1,\lambda _2,\ldots ,\lambda _n$ be its eigenvalues. The Estrada index of $G$ is a graph invariant defined as $EE=\sum _{i=1}^ne^{\lambda _i}$. We present a generic expression for $EE$ based on weights of short closed walks in $G$. We establish lower and upper bounds for $EE$in terms of low-order spectral moments involving the weights of closed walks. A concrete example of calculation is provided.

Keywords

Estrada indexweighted graphspectral momentgraph spectrum

MSC classification

Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 106 - 112
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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