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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 wellknown 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).doi:10.5614/ejgta.2015.3.2.3 fatcat:cyamycmgcvaetjrxzp2mkvx7ve