Almost every graph is vertex-oblique

The type of a vertex vv of a graph G   is the ordered degree sequence of the vertices adjacent to vv. The graph G   is called vertex-oblique if it contains no two vertices of the same type. We will show that almost every graph G∈G(n,p)G∈G(n,p) is vertex-oblique, if the probability p for each edge to appear in G is within certain bounds.