Back Edge Or Cross

Directed graph with edges 1→2, 1→3, 2→4, 3→4, 4→2. DFS starts at 1 and takes neighbours in increasing order. A clock ticks once per entry and once per exit:

vertex	pre	post
1	1	8
2	2	5
3	6	7
4	3	4

The tree edges are 1→2, 2→4, 1→3. Exactly one of the two remaining edges proves the graph contains a directed cycle. Which one, and what in the table proves it?

Both 3→4 and 4→2, so the graph has two distinct directed cycles.

4→2, because pre[2]=2 < pre[4]=3 < post[4]=4 < post[2]=5. Vertex 2 is still on the recursion stack when 4→2 is examined, so it is a back edge and closes the cycle 2 → 4 → 2.

3→4, because vertex 4 was already visited when the search reached 3, and an edge into an already-visited vertex is what a back edge means.

3→4, because post[4]=4 < pre[3]=6, and a target that finished before the source started is the definition of a back edge.