Lower bounds for Estrada index and Laplacian Estrada index. (English) Zbl 1203.05090
Summary: Let \(G\) be an \(n\)-vertex graph. If \(\lambda _{1},\lambda _{2},\dots ,\lambda _n\) and \(\mu _{1},\mu _{2},\dots ,\mu _n\) are the ordinary (adjacency) eigenvalues and the Laplacian eigenvalues of \(G\), respectively, then the Estrada index and the Laplacian Estrada index of \(G\) are defined as EE\((G) = \sum ^n_{i=1} e^{\lambda _{i}}\) and LEE\((G) = \sum ^n_{i=1} e^{\mu _{i}}\), respectively. Some new lower bounds for EE and LEE are obtained and shown to be the best possible.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
References:
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