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

Let the Kneser graph K of a distance-regular graph Γ be the graph on the same vertex set as Γ, where two vertices are adjacent when they have maximal distance in Γ. We study the situation where the Bose–Mesner algebra of Γ is not generated by the adjacency matrix of K. In particular, we obtain stron...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 480; pp. 115 - 126
Main Authors Brouwer, A.E., Fiol, M.A.
Format Journal Article Publication
LanguageEnglish
Published Elsevier Inc 01.09.2015
Elsevier
Subjects
Bose-Mesner algebra
Distance-regular graph
Grafs, Teoria de
Graph theory
Half-antipodality
Kneser graph
Matemàtica discreta
Matemàtiques i estadística
Teoria de grafs
Àlgebra
Àlgebra lineal i multilineal
Àrees temàtiques de la UPC
05E30
Distance-regular graph
Bose–Mesner algebra
05C50
Kneser graph
Half-antipodality
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Summary:Let the Kneser graph K of a distance-regular graph Γ be the graph on the same vertex set as Γ, where two vertices are adjacent when they have maximal distance in Γ. We study the situation where the Bose–Mesner algebra of Γ is not generated by the adjacency matrix of K. In particular, we obtain strong results in the so-called ‘half antipodal’ case.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2015.04.020