An undirected graph canbe converted into a directed graph by choosing a direction for every edge. Here is an example:
Show that for every undirected graph, there is a way of choosing directions for its edges so that the resulting directed graph has no directed cycles.
select any random vertex and start BFS algorithm such that if you are at vertex u and going to vertex v direction of the edge will be from u to v, u$\rightarrow$v, maintain a data structure visited[i] which keeps track of unvisited edge if the edge ek is visited we don't perform BFS this will create a directed graph with no back edge. complexity O(V+E)