The Normalized Laplacian Spectrum of Pentagonal Graphs and Its Applications

摘要

The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects,in particular those related to random walks.In this paper,we give the spectra of the normalized Laplacian of iterated pentagonal of a simple connected graph.As an application,we also find the significant formulae for their multiplicative degree-Kirchhoff index,Kemeny's constant and number of spanning trees.