On middle cube graphs
| Main Authors: | Dalfo, C.; Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Fiol, M. A.; Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Mitjana, M.; Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2015
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/126 http://www.ejgta.org/index.php/ejgta/article/view/126/pdf_6 |
Daftar Isi:
- 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).