MORE ON THE NORMALIZED LAPLACIAN ESTRADA INDEX

Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G) = Sigma(N)(i=1) e(lambda i-1,) where lambda(1), lambda(2), ... ,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 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.