Assign integers to the vertices of G

[mathmari]

Hey!

Let $G=(V,E)$ be a directed acyclic graph. I have to write an algorithm to assign integers to the vertices of $G$ such that if there is a directed edge from vertex $i$ to vertex $j$, then $i$ is less than $j$.Is it maybe as followed??

    L ← Set of integers
    S ← Set of all nodes with no incoming edges
    while S is non-empty do
        assign the lowest number i from L to first node n from S
        remove the node n from S
        remove the integer i from L
        for each node m with an edge e from n to m do
            remove edge e from the graph
            if m has no other incoming edges then
                insert m into S
    if graph has edges then
        return error (graph has at least one cycle)
    else 
        return G

Could you tell me if it correct?? (Wondering)

 

[Future Bruno]

Yes, your algorithm is correct. It will assign integers to the vertices of $G$ such that if there is a directed edge from vertex $i$ to vertex $j$, then $i$ is less than $j$.