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Distance-regular graphs where the distance-d graph has fewer distinct eigenvalues

Author
Fiol, M.; Brouwer, A.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2015-05-16
Volume
480
First page
115
Last page
126
DOI
https://doi.org/10.1016/j.laa.2015.04.020 Open in new window
Project funding
2009SGR1387
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
Repository
http://hdl.handle.net/2117/28555 Open in new window
Abstract
Let the Kneser graph K of a distance-regular graph $\Gamma$ be the graph on the same vertex set as $\Gamma$, where two vertices are adjacent when they have maximal distance in $\Gamma$. We study the situation where the Bose-Mesner algebra of $\Gamma$ is not generated by the adjacency matrix of K. In particular, we obtain strong results in the so-called `half antipodal' case.
Citation
Fiol, M.; Brouwer, A. Distance-regular graphs where the distance-d graph has fewer distinct eigenvalues. "Linear algebra and its applications", 2015, vol. 480, p. 115-126.
Keywords
Bose-Mesner algebra, Distance-regular graph, Kneser graph, half-antipodality.
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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