Is the result of topological ordering unique?
Take the example of the ordering of the several integers stored in the array.
If all the integers in the array are different, then the ordering of all elements according to the size is certain, that is, this sequence satisfies total order relation. For a structure with total order, the result after its linearization (ordering) is certain to be unique.
If there are integers of the same value in the array, the relation between elements with the same value cannot be determined. Therefore, they can appear in arbitrary order in the final ordering result.
For elements with the same value, if we specify that the one that appears earlier is bigger than the one that appears later, then we can convert the partial order to a total order, obtaining a unique result.
Expanding it to topological ordering, the condition for the result to be unique is that all vertices have a complete order relation among them. If there is no complete order relation, then the result of the topological ordering would not be unique.
For →Fig. 2.61, there are multiple topological ordering sequences. We list two of them: (C1，C3，C2，C6，C4， C5) and (C6，C1，C3，C2，C4，C5).