(0, ½, 1) matrices which are extreme points of the generalized transitive tournament polytope

Abstract Following Brualdi and Hwang, given a generalized transitive tournament (GTT) matrix T of order n , we consider the *-graph of T , that is, the undirected graph with vertices 1, 2, …, n in which there is an edge { i , j } between vertices i and j if and only if 0 ij . We characterize the *-graphs of the extreme GTT (0, ½, 1) matrices of order n . Using this characterization, we obtain for n = 6, 7 the complete list of extreme GTT (0, ½, 1) matrices of order n .