The (1,2)(1,2)-step competition graph of a pure local tournament that is not round decomposable

The competition graph of a digraph was introduced by Cohen in 1968 associated with the study of ecosystems. In 2011, Factor et al. (2011), defined the (1,2)(1,2)-step competition graph of a digraph which is a generalization of the competition graph and gave a characterization of the (1,2)(1,2)-step competition graph of a tournament. In this paper, we characterize the (1,2)(1,2)-step competition graph of a pure local tournament that is not round decomposable.