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ESTRADA INDEX OF GENERAL WEIGHTED GRAPHS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 88 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 28 September 2012, pp. 106-112
- Print publication:
- August 2013
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- Article
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- You have access
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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.
