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It is established that up to isomorphism,there are only one (K_4-e)-design oforder 6, three (K_4-e)-designs of order 10 and two (K_4-e)-designs of order 11.As an application of our enumerative results, we discuss the fine triangleintersection problem for (K_4-e)-designs of orders v=6,10,11.

Enumerations of (K_4-e)-designs with small orders