Changing the order in which the vertices are processed can change the spanning tree created when running Depth-First Search Algorithm

Yes, changing the order in which the vertices are processed can indeed change the spanning tree created when running the Depth-First Search (DFS) Algorithm. Here's why:

1. The DFS algorithm works by starting at a root node, then exploring as far as possible along each branch before backtracking.

2. The order in which vertices are processed is determined by the order in which they are discovered. The first vertex discovered is the root, and the next vertices discovered are those directly connected to the root, and so on.

3. If you change the order in which vertices are processed, you're essentially changing the order in which they are discovered. This means you could end up with a different root, or different branches being explored first.

4. As a result, the spanning tree - which is a tree that connects all the vertices in a graph without any cycles - could end up looking different. The vertices and edges would be the same, but the layout or "shape" of the tree could change.

5. However, it's important to note that while the spanning tree may look different, it would still be a valid spanning tree. The DFS algorithm guarantees that all vertices will be connected and that there will be no cycles, regardless of the order in which vertices are processed.