Extremal oriented graphs avoiding 1-subdivision of an in-star

An oriented graph is a digraph obtained from an undirected graph by choosing an orientation for each edge. Given a positive integer n and an oriented graph F, the oriented Turan number exₒᵣᵢ(n,F) is the maximum number of arcs in an F-free oriented graph of order n. In this paper, we investigate the oriented Turan number exₒᵣᵢ(n, Sk,1 ), where Sk,1 is the $1$-subdivision of the in-star of order $k+1$. We determine exₒᵣᵢ(n,Sk,1) for $k=2,3$ as well as the extremal oriented graphs. For k≥ 4, we establish a lower bound and an upper bound on exₒᵣᵢ(n,Sk,1).