The vector space of so-called "A_like" matrices of a hypercube is decomposed into the direct sum of its symmetric part and antisymmetric part. A basis for each part is given.
Let G be a bipartite distance-regular graph and let x,y be vertices of G at distance 2. Let W denote the vector space spanned by the characteristic vectors of the distance partition of the vertex set of G with respect to vertices x,y. In this paper we study the vector space MW which consist of all products mw, where w is a vector from W and m iz a matrix from the Bose-mesner algebra of G. An orthogonal basis for MW is given and the square norms of the vectors of this basis are given. The action of adjacency matrix of G on the vectors of this basis is given.
In this paper the Cayley graphs on dihedral groups which have a group of automorphisms which act regularly on the arc set of the given graph are studied.