Abstract
LetTm be the adjacency matrix of the triangular graph. We will give conditions for a linear combination ofTm, I andJ to be decomposable. This leads to Bruck-Ryser-Chowla like conditions for, what we call, triangular designs. These are quasi-symmetric designs whose block graph is the complement of the triangular graph. For these designs our conditions turn out to be stronger than the known non-existence results for quasi-symmetric designs.
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