Brouwer, Andries E.; Pasechnik, Dmitrii V. Two distance-regular graphs. (English) Zbl 1254.05199 J. Algebr. Comb. 36, No. 3, 403-407 (2012). In this paper two families of distance-regular graphs, the subgraph of the dual polar graph of type \(B_{3}(q)\) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type \(D_{4}(q)\) induced on the vertices far from a fixed edge are constructed. The first graph is defined as follows: let \(W\) be a vector space of dimension 3 over the field \(F_{q}\), provided with an outer product \(\times\). Let \(Z\) be the graph with vertex set \(W\times W\) where \((u,u')\) is adjacent to \((v,v')\) if and only if \((u,u')\neq (v,v')\) and \(u \times v+u'-v'=0\). Then \(Z\) is distance-regular of diameter 3 on \(q^{6}\) vertices. The latter is the extended bipartite double of the former. Reviewer: Ioan Tomescu (Bucureşti) Cited in 3 Documents MSC: 05E30 Association schemes, strongly regular graphs 05C12 Distance in graphs Keywords:distance-regular graph; dual polar graph; extended bipartite double; Buckenhout-Tits diagram; intersection array PDFBibTeX XMLCite \textit{A. E. Brouwer} and \textit{D. V. Pasechnik}, J. Algebr. Comb. 36, No. 3, 403--407 (2012; Zbl 1254.05199) Full Text: DOI arXiv References: [1] Blok, R.J., Brouwer, A.E.: The geometry far from a residue. In: di Martino, L., Kantor, W.M., Lunardon, G., Pasini, A., Tamburini, M.C. (eds.) Groups and Geometries, pp. 29–38. Birkhäuser, Basel (1998) · Zbl 0899.51005 [2] Brouwer, A.E.: Additions and corrections to [3]. http://www.win.tue.nl/\(\sim\)aeb/drg/index.html [3] Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer, Heidelberg (1989) · Zbl 0747.05073 [4] Pasini, A.: Diagram Geometries. Oxford University Press, Oxford (1994) · Zbl 0813.51002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.