Corpus ID: 9945449

Universality for Barycentric subdivision

@article{Knill2015UniversalityFB,
  title={Universality for Barycentric subdivision},
  author={O. Knill},
  journal={ArXiv},
  year={2015},
  volume={abs/1509.06092}
}
  • O. Knill
  • Published 2015
  • Mathematics, Computer Science
  • ArXiv
  • The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. The proof uses an explicit linear operator mapping the clique vector of a graph to the clique vector of the Barycentric refinement. The eigenvectors of its transpose produce integral geometric invariants for which Euler characteristic is one example. 
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