Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646655 | Discrete Mathematics | 2016 | 18 Pages |
Abstract
Let Γ=Γ(2n,q)Γ=Γ(2n,q) be the dual polar graph of type Sp(2n,q)Sp(2n,q). Underlying this graph is a 2n2n-dimensional vector space VV over a field FqFq of odd order qq, together with a symplectic (i.e. nondegenerate alternating bilinear) form B:V×V→FqB:V×V→Fq. The vertex set of ΓΓ is the set VV of all nn-dimensional totally isotropic subspaces of VV. If q≡1q≡1 mod 4, we obtain from ΓΓ a nontrivial two-graph Δ=Δ(2n,q)Δ=Δ(2n,q) on VV invariant under PSp(2n,q)PSp(2n,q). This two-graph corresponds to a double cover Γ̂→Γ on which is naturally defined a QQ-polynomial (2n+1)(2n+1)-class association scheme on 2|V̂| vertices.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
G. Eric Moorhouse, Jason Williford,