Projective non-commuting graph of a group

Let G be a finite non-abelian group and let T be a transversal of the center of G in G. The non-commuting graph of G on a transversal of the center is the graph whose vertices are the non-central elements of T and two vertices x and y are joined by an edge whenever xy ≠ yx. In this paper, we classify the groups whose non-commuting graph on a transversal of the center is projective.