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 e?i?1, where ?1, ?2,... , ?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 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.