I have a homework problem I think I know the answer to, but want to double check
Consider the graph with three nodes, $a$, $b$, and $c$, and the two arcs $a \rightarrow b$ and $b \rightarrow c$. Give all the possible depth-first search forests for this graph, considering all possible starting nodes for each tree. What is the postorder numbering of the nodes for each forest? Are the postorder numbers always the same for this graph?
I know what to do for DFS, but I am unsure whether or not there will be multiple trees for this example. I do not see how there could be. If you start at node a, you will immediately go to c, giving (c,b,a). Start at b, you will get the same thing, etc.
Am I thinking of this correctly?