More on the normalized Laplacian Estrada index

Abstract

Let $G$ be a simple graph of order $N$. The normalized Laplacian Estrada index of $G$ is defined as $NEE(G)={\sum }_{i=1}^N{e}^{{\lambda }_i}$, where ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_N$ are the normalized Laplacian eigenvalues of $G$. In this paper, we give a tight lower bound for $NEE$ of general graphs. We also calculate $NEE$ for a class of treelike fractals, which contain some classical chemical trees as special cases. It is shown that $NEE$ scales linearly with the order of the fractal, in line with a best possible lower bound for connected bipartite graphs.

12 pages

References in corpus (4)

• Subgraph Centrality in Complex Networks
• Spectral Measures of Bipartivity in Complex Networks
• Determining mean first-passage time on a class of treelike regular fractals
• The Decimation Method for Laplacians on Fractals: Spectra and Complex Dynamics