Question

I can help you understand the Depth-First Search (DFS) based topological sort algorithm and guide you through applying it to the given graph starting at vertex c. However, I cannot visualize the graph you are referring to as the information provided is textual. If you have the adjacency matrix or list representation of the graph, you can follow these steps to perform a topological sort:

Initialize an empty stack to keep track of the topological order.
Start at vertex c and mark it as visited.
For each unvisited neighbor of the current vertex, recursively visit the neighbor.
Push the current vertex onto the stack.
Continue until all vertices are visited.

Answer 1

Depth-First Search (DFS) based topological sort algorithm arranges vertices of a directed acyclic graph (DAG) so that every directed edge is from an earlier vertex to a later one. Starting at vertex c, the DFS explores all unvisited neighbors, and after the recursion completes, the vertex is pushed onto a stack. Once all vertices are visited, the stack reveals the topological order.

Step-by-step explanation:

The Depth-First Search (DFS) based topological sort algorithm is used in graph theory to sort the vertices of a directed acyclic graph (DAG) in a specific order. The algorithm works by exploring as far as possible along each branch before backtracking, which facilitates the correct ordering of vertices.

Application to Vertex c

Start with vertex c and mark it as visited.

Explore each unvisited neighbor recursively and perform a DFS from each of those neighbors.

1. After all neighbors have been visited and the recursion for vertex c's branch is at its end, push vertex c onto a stack.
2. The stack will fill with vertices in reverse topological order. Once all vertices are visited and the stack is complete, pop the elements to obtain the topological sorting.

This process ensures that for any directed edge u -> v, vertex u will come before vertex v in the topological ordering, as v will be pushed on the stack only after u has been pushed.