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 Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.     

Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces

Mathematical Notes -     

Mathematical Aspects of the Heap Paradox and the Hidden Parameter

Mathematical Notes -     

Efficient Tosylation of Dihydroxybenzenes in a Two-Phase Water–Dichloromethane System

Theoretical and Experimental Chemistry - The effect of the structure of the catalyst and the type of base on the reaction rate and product yield of the tosylation of dihydroxybenzenes in a...