Prove that every acyclic graph has at least one source vertex and at least one termination vertex How can i prove that every acyclic graph has at least one source vertex and one(at least) termination vertex? 
 A: My suggestion is: that P=(u,…v)  is the maximum path of the graph D.If a vertex u is adjacent to one vertex of P, then i have a cyrcle. So its wrong. If vertex u is adjacent to one vertex which dont belong to P, then i have a new bigger path. So the vertex is not neighboring an other vertex and d(u) = 0 
A: Suppose not.  Then either, your graph has no sources or your graph has no sinks.  Let's assume for a minute that it has no sinks.  Pick a random vertex as a starting point.  Walk around your graph following directed edges.  There are no sinks, so you can always continue walking.  But you are in a finite graph, so the pigeonhole principle says you will eventually hit the same vertex twice.  That means you walked in a cycle, which is a contradiction.
If there are no sources, then replace your graph with a new one where you give every edge the opposite orientation.  Now you have a graph with no sinks.  The above argument gives a cycle in that graph.  If you turn all the edges back around, you still have a cycle.
