The (1, 2)-step competition graph of a hypertournament

Abstract In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the ( 1 , 2 ) \left(1,2) -step competition graph of a digraph. Given digraph D = V A D=\left(V,A) , D denoted C {C}_{1,2}\left(D) is on V\left(D) where x y ∈ E xy\in E\left({C}_{1,2}\left(D)) if only there exists vertex z ≠ z\ne x,y such that either d − {d}_{D-y}\left(x,z)=1 ≤ {d}_{D-x}(y,z)\le 2 or {d}_{D-x}(y,z)=1 {d}_{D-y}\left(x,z)\le . They also characterized (1, 2)-step graphs tournaments extended some results to i j \left(i,j) tournaments. this paper, definition generalized hypertournament k -hypertournament characterized. Also, are -hypertournaments.