More on the normalized Laplacian Estrada index

2014/01/07 by Yilun Shang, Shang, Yilun
Mathematics · #05C05 #05C50 #05C90 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory (math.SP) #math.CO #math.SP #msc:05C05 #msc:05C50 #msc:05C90 #msc:15A18

paper · pdf · doi:10.48550/arxiv.1401.1263

12 pages

arxiv created 2014/01/07 · arxiv updated 2014/01/08

Abstract

Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G)=∑_i=1^Ne^λ_i, where λ₁,λ₂,⋯,λ_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.

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