More on the normalized Laplacian Estrada index

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Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G)=∑ᵢ₌₁ⁿeλⁱ, 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 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.