Balasubramanian K. Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes.
JOURNAL OF MATHEMATICAL CHEMISTRY 2023;
61:1-22. [PMID:
37360905 PMCID:
PMC10129317 DOI:
10.1007/s10910-023-01479-3]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 04/06/2023] [Indexed: 06/28/2023]
Abstract
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
Collapse