Corpus ID: 11626507

The graph spectrum of barycentric refinements

@article{Knill2015TheGS,
  title={The graph spectrum of barycentric refinements},
  author={O. Knill},
  journal={ArXiv},
  year={2015},
  volume={abs/1508.02027}
}
  • O. Knill
  • Published 2015
  • Computer Science, Mathematics
  • ArXiv
  • Given a finite simple graph G, let G' be its barycentric refinement: it is the graph in which the vertices are the complete subgraphs of G and in which two such subgraphs are connected, if one is contained into the other. If L(0)=0 = dim(G). Let G(m) be the sequence of barycentric refinements of G=G(0). We prove that for any finite simple graph G, the spectral functions F(G(m)) of successive refinements converge for m to infinity uniformly on compact subsets of (0,1) and exponentially fast to a… CONTINUE READING
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