Bipartite distance-regular graphs and taut pairs of pseudo primitive idempotents
Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 499-520.

Let Γ denote a bipartite distance-regular graph with diameter D4, valency k3, and intersection numbers c i ,b i (0iD). By a pseudo cosine sequence of Γ we mean a sequence of complex scalars σ 0 ,σ 1 ,...,σ D such that σ 0 =1 and c i σ i-1 +b i σ i+1 =kσ 1 σ i for 1iD-1. By an associated pseudo primitive idempotent of Γ, we mean a nonzero scalar multiple of the matrix i=0 D σ i A i , where A 0 ,A 1 ,...,A D are the distance matrices of Γ. Given pseudo primitive idempotents E,F of Γ, we define the pair E,F to be taut whenever the entry-wise product EF is not a scalar multiple of a pseudo primitive idempotent, but is a linear combination of two pseudo primitive idempotents of Γ. In this paper, we determine all the taut pairs of pseudo primitive idempotents of Γ.

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DOI: 10.5802/alco.51
Classification: 05E30
Keywords: distance-regular graph, pseudo primitive idempotent, taut pair
MacLean, Mark S. 1; Miklavič, Štefko 2

1 Mathematics Department Seattle University 901 Twelfth Avenue Seattle WA 98122-1090, USA
2 University of Primorska Andrej Marušič Institute Muzejski trg 2 6000 Koper, Slovenia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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MacLean, Mark S.; Miklavič, Štefko. Bipartite distance-regular graphs and taut pairs of pseudo primitive idempotents. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 499-520. doi : 10.5802/alco.51. https://alco.centre-mersenne.org/articles/10.5802/alco.51/

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