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Title: Digraphs in which every t vertices have exactly λ common out-neighbors

Abstract: We say that a digraph is a (t, lambda)-liking digraph if every t vertices have exactly lambda common out-neighbors. In 1975, Plesnik (1975) [14] proved that any (t,1)-liking digraph is the complete digraph on t + 1 vertices for each t >= 3. Choi et al. (2025) [5] showed that a (2,1)-liking digraph is a fancy wheel digraph or a k-diregular digraph for some positive integer k. In this paper, we extend these results by completely characterizing the (t, lambda)-liking digraphs with t >= lambda+2 and giving some equivalent conditions for a (t, lambda)-liking digraph being a complete digraph on t + lambda vertices.

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