interface GraphInterface {
 
  // determine number of vertices in the graph
  public int getNumVertices();
  
  // determine number of edges in the graph
  public int getNumEdges();

  // determine if there is an edge between vertex v and vertex w
  public boolean isEdge(int v, int w);

  // add an edge from vertex v to vertex w
  public void addEdge(int v, int w);
    
  // remove the edge from vertex v to vertex w
  public void removeEdge(int v, int w);

}