The Normalized Laplacian Spectrum of Folded Hypercube with Applications

Abstract

In this work, we determine all the eigenvalues and their corresponding multiplicities of the normalized Laplacian matrix for folded hypercubes. Furthermore, we establish the explicit formula to calculate Kemeny’s constant for random walks on the folded hypercube, which indicates that its growth is roughly consistent with the network order. In addition, we also determine the number of spanning trees and degree-Kirchhoff index of folded hypercubes. Especially, we make some comparisons with that of hypercubes to verify that folded hypercubes have superior properties than hypercubes.