Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes

  title={Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes},
  author={Hajime Tanaka and Rie Tanaka},
  journal={Eur. J. Comb.},
On few-class Q-polynomial association schemes: feasible parameters and nonexistence results
We present the tables of feasible parameters of primitive $3$-class $Q$-polynomial association schemes and $4$- and $5$-class $Q$-bipartite association schemes (on up to $2800$, $10000$, and $50000$
Twice Q-polynomial distance-regular graphs of diameter 4
It is known that a distance-regular graph with valency k at least three admits at most two Q-polynomial structures. We show that all distance-regular graphs with diameter four and valency at least
On Q-Polynomial Association Schemes of Small Class
  • Sho Suda
  • Mathematics
    Electron. J. Comb.
  • 2012
An inequality involving the third largest or second smallest dual eigenvalues of $Q$-polynomial association schemes of class at least three is shown and can be applied to distance-regular graphs as well.
Cometric Association Schemes.
One may think of a $d$-class association scheme as a $(d+1)$-dimensional matrix algebra over $\mathbb{R}$ closed under Schur products. In this context, an imprimitive scheme is one which admits a
Distance-regular graphs
An introduction to distance-regular graphs is presented for the reader who is unfamiliar with the subject, and an overview of some developments in the area of distance- regular graphs since the monograph 'BCN' was written.
On the Connectivity of Graphs in Association Schemes
It is proved that the deletion of the neighborhood of any vertex leaves behind at most one non-singleton component, and the only connected relations in symmetric association schemes which admit a disconnecting set of size two are those which are ordinary polygons.
Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry
In this paper we show that if θ is a T -design of an association scheme (Ω , R ), and the Krein parameters q hi,j vanish for some h 6∈ T and all i, j 6∈ T ( i, j, h 6 = 0), then θ consists of


Non-existence of imprimitive Q-polynomial schemes of exceptional type with d=4
Commutative association schemes
A survey on spherical designs and algebraic combinatorics on spheres
Imprimitive Q-polynomial Association Schemes
AbstractIt is well known that imprimitive P-polynomial association schemes $$\mathcal{X} = (X,\{ R_i \} _{0 \leqslant i \leqslant d} ) $$ with $$$$ are either bipartite or antipodal, i.e.,
Distance-Regular Graphs
Algebraic Combinatorics I: Association Schemes