The image-step competition graph of a tournament Original Research Article

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the image-step competition graph. In this paper, we offer another generalization of the competition graph. We define the image-step competition graph of a digraph image, denoted image, as the graph on image where image if and only if there exists a vertex image, such that either image and image or image and image. In this paper, we characterize the image-step competition graphs of tournaments and extend our results to the image-step competition graph of a tournament.