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Suppose you are performing a BFS on the following graph, starting on node 0: In which of the following orders are the nodes visited, assuming that the BFS algorithm produces neighbors in numerical order?

Choice 1 of 4:0, 1, 2, 3, 4, 5

Choice 2 of 4:0, 1, 3, 5, 4, 2

Choice 3 of 4:0, 1, 3, 4, 5, 2

Choice 4 of 4:0, 3, 1, 4, 5, 2

To determine the order in which nodes are visited during a Breadth-First Search (BFS) starting from node 0, let's go through the process step by step.

### BFS Process:
1. **Start at node 0**: Node 0 is the starting point, so it's the first node visited.
2. **Visit neighbors of node 0**: The neighbors of node 0 are nodes 1, 3, and 4. Since BFS explores nodes level by level, and neighbors are visited in numerical order, node 1 is visited first, followed by node 3 and then node 4.
3. **Visit neighbors of node 1**: Node 1 has neighbors 0, 4, and 5. Node 0 has already been visited, so we visit the next unvisited node in numerical order, which is node 5.
4. **Visit neighbors of node 3**: Node 3 has neighbors 0 and 4. Both have already been visited, so no new nodes are visited at this step.
5. **Visit neighbors of node 4**: Node 4 has neighbors 1, 2, 3, and 0. Nodes 1, 3, and 0 have already been visited, so the next unvisited node in numerical order is node 2.
6. **Visit neighbors of node 5**: Node 5 has neighbors 1 and 4. Both have already been visited.

### Conclusion:
The BFS order is **0, 1, 3, 4, 5, 2**.

So, the correct choice is **Choice 3**: **0, 1, 3, 4, 5, 2**.

Would you like more details or have any other questions? Here are some related topics:

1. How does BFS ensure the shortest path in unweighted graphs?
2. What is the difference between BFS and Depth-First Search (DFS)?
3. How would the BFS order change if we start from a different node?
4. What is the time complexity of the BFS algorithm?
5. How can BFS be modified for different traversal orders?

**Tip:** In BFS, always remember that nodes are visited level by level, and the order of visiting neighbors can affect the final traversal order.

Explore the Breadth-First Search (BFS) algorithm on a graph starting from node 0. Learn the order in which nodes are visited with a step-by-step explanation. This problem covers key concepts in graph theory and BFS traversal.

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