On Middle Cube Graphs

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...

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Bibliographic Details
Published inElectronic journal of graph theory and applications Vol. 3; no. 2; pp. 133 - 145
Main Authors Dalfo, Cristina, Fiola, Miquel Angel, Mitjana, Margarida
Format Journal Article Publication
LanguageEnglish
Published Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 01.10.2015
Subjects
distance-regular graph
distance-regular graph, odd graph, spectrum
Grafs, Teoria de
Graph theory
Matemàtiques i estadística
odd graph
spectrum
Àrees temàtiques de la UPC
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Summary: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).
ISSN:2338-2287
2338-2287
DOI:10.5614/ejgta.2015.3.2.3