Abstract
A quasi-symmetric design (QSD) is a (v,k,λ) design with two intersection numbers x,y, where 0≤x<y<k. The block graph of QSD is a strongly regular graph (SRG). It is known that there are SRGs which are not block graphs of QSDs. We derive necessary conditions on the parameters of a SRG to be feasible as the block graph of a QSD. We apply these conditions to rule out many infinite families of such SRGs.We also show that the pseudo Latin square graph L5(n), n≥5; the Negative Latin square graphs NLe(e2+3e) and NLe(e+2), with 2≤e or their complements cannot be the block graph of a QSD.
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