 Any undirected graph may be made into a DAG by choosing a total order for its vertices and directing every edge from the earlier endpoint in the order to the later endpoint . The resulting orientation of the edges is called an acyclic orientation . Different total orders may lead to the same acyclic orientation , so an n @-@ vertex graph can have fewer than n ! acyclic orientations . The number of acyclic orientations is equal to | <unk> ( − 1 ) | , where <unk> is the <unk> polynomial of the given graph . 
