On Bipartite $Q$-Polynomial Distance-Regular Graphs with $c_2 \le 2$

Stefko Miklavic, Safet Penjic

Abstract


Let $\Gamma$ denote a bipartite $Q$-polynomial distance-regular graph with diameter $D \ge 4$, valency $k \ge 3$ and intersection number $c_2 \le 2$. We show that $\Gamma$ is either the $D$-dimensional hypercube, or the antipodal quotient of the $2D$-dimensional hypercube, or $D=5$.


Keywords


Distance-regular graphs; Q-polynomial property; Equitable partitions

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