1. Prove that a graph-traversal algorithm visits every vertex in the graph if and only if the graph is connected, regardless of where the traversal starts. 2. Although the DFS traversal algorithm has...

1. Prove that a graph-traversal algorithm visits every vertex in the graph if and only if the graph is connected, regardless of where the traversal starts.

2. Although the DFS traversal algorithm has a simple recursive form, a recursive BFS traversal algorithm is not straightforward.

a. Explain why this statement is true.

b. Write the pseudocode for a recursive version of the BFS traversal algorithm.