On the Minimum Degree Up to Local Complementation: Bounds and Complexity

@article{Javelle2012OnTM,
  title={On the Minimum Degree Up to Local Complementation: Bounds and Complexity},
  author={J{\'e}r{\^o}me Javelle and Mehdi Mhalla and Simon Perdrix},
  journal={ArXiv},
  year={2012},
  volume={abs/1204.4564}
}
  • Jérôme Javelle, Mehdi Mhalla, Simon Perdrix
  • Published in WG 2012
  • Mathematics, Computer Science, Physics
  • ArXiv
  • The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than $\sqrt{p} - \frac{3}{2}$, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive… CONTINUE READING

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