Estrada index of general weighted graphs

Authors

  • Y. Shang University of Texas at San Antonio

Keywords:

Estrada index, graph spectrum

Abstract

Let $G$ be a general weighted graph (with possible self-loops) on $n$ vertices and $\lambda_1,\lambda_2,\cdots,\lambda_n$ 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 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. 10.1017/S0004972712000676

Author Biography

Y. Shang, University of Texas at San Antonio

Institute for Cyber Security, Mathematics Department

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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