English

On middle cube graphs

Combinatorics 2016-08-12 v1

Abstract

We study a family of graphs related to the nn-cube. The middle cube graph of parameter kk is the subgraph of Q2k1Q_{2k-1} induced by the set of vertices whose binary representation has either k1k-1 or kk 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 (eigenvalues and their multiplicities, and associated eigenvectors).

Keywords

Cite

@article{arxiv.1608.03551,
  title  = {On middle cube graphs},
  author = {C. Dalfó and M. A. Fiol and M. Mitjana},
  journal= {arXiv preprint arXiv:1608.03551},
  year   = {2016}
}
R2 v1 2026-06-22T15:17:51.682Z