Description
Let \Gamma denote a Q-polynomial bipartite distance-regular graph with diameter D, valency k \ge 3 and intersection number c_2\le 2. In this talk we show the following two results:
(1) If D \ge 6, then \Gamma is either the D-dimensional hypercube, or the antipodal quotient of the 2D-dimensional hypercube.
(2) If D = 4 and c_2\le 2 then \Gamma is either the 4-dimensional hypercube, or the antipodal quotient of the 8-dimensional hypercube.
We show (1) using results of Caughman. To show (2) we first introduce certain equitable partition of the vertex-set of \Gamma. Then we use this equitable partition to prove (2).
Primary author
Mr
Safet Penjich
(University of Primorska)
