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) =∑Ni=1 eλi-1, where λ1, λ2, · · · λN 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 contains T fractal and Peano basin fractal as its limiting 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.