On middle cube graphs

C. Dalfo, M. A. Fiol, M. Mitjana


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 (eigenvalues and their multiplicities, and associated eigenvectors).


distance-regular graph, odd graph, spectrum

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DOI: http://dx.doi.org/10.5614/ejgta.2015.3.2.3


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ISSN: 2338-2287

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