# 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} }

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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