Generalized designs on graphs: Sampling, spectra, symmetries

@article{Steinerberger2020GeneralizedDO,
  title={Generalized designs on graphs: Sampling, spectra, symmetries},
  author={Stefan Steinerberger},
  journal={Journal of Graph Theory},
  year={2020},
  volume={93},
  pages={253-267}
}
  • Stefan Steinerberger
  • Published 2020
  • Computer Science, Mathematics
  • Journal of Graph Theory
  • Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They are evenly distributed and often exhibit a great degree of regularity and symmetry. We point out that a spectral definition of spherical designs easily transfers to finite graphs -- these 'graphical designs' are subsets of vertices that are evenly spaced and… CONTINUE READING

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