Dependency Graphs Math Example 2

Solution

1. 1
   Identify edges: $A \to D$, $B \to D$, $B \to E$, $C \to E$, $D \to F$, $E \to F$.
2. 2
   Nodes with no incoming edges (sources): $A$, $B$, $C$. These can appear in any order among themselves at the start.
3. 3
   After removing $A$, $B$, $C$: node $D$ depends on $A, B$ (done) and $E$ depends on $B, C$ (done), so $D$ and $E$ can appear in either order.
4. 4
   Finally $F$ must come last since it depends on both $D$ and $E$.
5. 5
   Valid orderings include: $(A, B, C, D, E, F)$, $(A, C, B, D, E, F)$, $(B, A, C, E, D, F)$, $(C, B, A, E, D, F)$, and others where the dependency constraints are satisfied.