The (1, 2)-step competition graph of a hypertournament
Ruijuan Li, Xiaoting An, Xinhong Zhang · Open Mathematics · 2021
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 a digraph D = ( V , A ) D=\left(V,A) , the ( 1 , 2 ) \left(1,2) -step competition graph of D, denoted C 1 , 2 ( D ) {C}_{1,2}\left(D) , is a graph on V ( D ) V\left(D) , where x y ∈ E ( C 1 , 2 ( D ) ) xy\in E\left({C}_{1,2}\left(D)) if and only if there exists a vertex z ≠ x , y z e x,y such that either d D − y ( x , z ) = 1 {d}_{D-y}\left(x,z)=1 and d D − x ( y , z ) ≤ 2