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## On middle cube graphs

Author
Dalfo, C.; Fiol, M.; Mitjana, M.
Type of activity
Journal article
Journal
Electronic journal of graph theory and applications
Date of publication
2015
Volume
3
Number
2
First page
133
Last page
145
DOI
https://doi.org/10.5614/ejgta.2015.3.2.3
Project funding
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
Repository
http://hdl.handle.net/2117/85344
URL
http://ejgta.org/index.php/ejgta/
Abstract
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 (eigenvalu...
Citation
Dalfo, C., Fiol, M., Mitjana, M. On middle cube graphs. "Electronic Journal of Graph Theory and Applications", 2015, vol. 3, núm. 2, p. 133-145.
Keywords
distance-regular graph, odd graph, spectrum
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
MAPTHE - Matrix Analysis and Discrete Potential Theory