Abstract
In this paper we define a regular m-partition of a distance regular graph as a partition of the vertex set into m classes, such that the number of vertices of a given class adjacent to a fixed vertex of another class (but possibly the same), is independent of the choice of that vertex in this class. Furthermore, we exhibit a technique to determine exact, discrete or bounding values for the intersection numbers of two such regular partitions of a DRG. As an application, we perform a structural investigation on the substructures of finite generalized polygons and, besides some new results, we give unifying, alternative and more elegant proofs of the results in Offer (J Combin Theory Ser A 97: 184–186, 2002) and Offer (Discrete Math 294: 147–160, 2005).
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The first author is a Postdoctoral Fellow of the Fund for Scientific Research—Flanders (Belgium) (F.W.O.).
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De Wispelaere, A., Van Maldeghem, H. Regular partitions of (weak) finite generalized polygons. Des. Codes Cryptogr. 47, 53–73 (2008). https://doi.org/10.1007/s10623-007-9062-9
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DOI: https://doi.org/10.1007/s10623-007-9062-9