Every tournament T of order at least 3 admits infinitely many T-irregular oriented graphs

Let F be a fixed graph. A graph G is F-irregular if any two distinct vertices of G belong to a different number of subgraphs of G isomorphic to F. In this paper, we settle the strong conjecture about F-irregular oriented graphs (Dovzhenok, Lukashenko, and Filiuta, 2026) for the case of tournaments. Specifically, we prove that for every tournament T of order n ≥ 3, there exists an infinite family of T-irregular oriented graphs. Our proof is constructive. For n ≥ 4, it is based on the vertex cloning method, and the underlying graphs of the constructed T-irregular oriented graphs are inherently Kₙ-irregular.