On middle cube graphs

@article{Dalf2015OnMC,
  title={On middle cube graphs},
  author={Cristina Dalf{\'o} and Miguel Angel Fiol and Margarida Mitjana},
  journal={Electron. J. Graph Theory Appl.},
  year={2015},
  volume={3},
  pages={133-145}
}
We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra… 

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