(a). Determine the DFS tree of K3,3.

(b). Determine the BFS tree of K3,3.

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To determine the DFS tree and BFS tree of K3,3, we first need to understand what K3,3 represents. K3,3 is a complete bipartite graph that consists of two sets of vertices, each containing three vertices, and every vertex in one set is connected to every vertex in the other set.

Now, let's find the DFS tree and BFS tree for K3,3.

(a) Determining the DFS tree of K3,3:
1. Start with any arbitrary vertex as the root of the DFS tree.
2. Choose one of the sets of vertices in K3,3 as the starting point and mark it as visited.
3. Explore all the adjacent vertices that are not yet visited. Pick one of them as the next vertex and mark it as visited.
4. Repeat step 3 until you have visited all the vertices.

The DFS tree is a tree that represents the order in which vertices are visited during the depth-first search. Since K3,3 is a complete bipartite graph, the exact tree structure will differ based on the starting vertex and the choices made at each step.

(b) Determining the BFS tree of K3,3:
1. Start with any arbitrary vertex as the root of the BFS tree and set its level as 0.
2. Assign level 1 to all the neighboring vertices of the root.
3. Assign level 2 to all the vertices connected to the level 1 vertices, but not yet assigned a level.
4. Continue this process until all vertices are assigned levels, visiting the vertices in a breadth-first manner.

The BFS tree is a tree that represents the tree structure created during the breadth-first search. Again, since K3,3 is a complete bipartite graph, the exact tree structure will depend on the starting vertex and the choices made at each step.

Note: K3,3 is not a connected graph, so it would have multiple disconnected components. Each component can have its own DFS tree and BFS tree.