Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes

Abstract

We obtain the characteristic polynomials and a number of spectral-based indices such as the Riemann-Zeta functional indices and spectral entropies of n-dimensional hypercubes using recursive Hadamard transforms. The computed numerical results are constructed for up to 23-dimensional hypercubes. While the graph energies exhibit a J-curve as a function of the dimension of the n-cubes, the spectra-based entropies exhibit a linear dependence on the dimension. We have also provided structural interpretations for the coefficients of the characteristic polynomials of n-cubes and obtain expressions for the integer sequences formed by the spectral-based Riemann-Zeta functions. Graphical abstract

On Laplacian Eigenvalues of Wheel Graphs

“…Q(G) is the graph created from G by joining a new vertex to every edge of G and by joining the edges of those pairs of new vertices that lie on adjacent edges of G. The Laplacian polynomials of R(G) and Q(G) of a regular graph G were derived, along with a formula and the lower bounds of the Kirchhoff index of these graphs. In 2023, Balasubramanian [15] obtained the characteristic polynomials and a number of spectral-based indices such as the Riemann-Zeta functional indices and spectral entropies of n-dimensional hypercubes using recursive Hadamard transforms. In [16], the same author used the Hadamard symmetry and recursive dynamic computational techniques to obtain a large number of degree-and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, and entropies and the matching polynomials of n-dimensional hypercubes.…”