The paths in the tree T produced by breadthfirst traversal a

The paths in the tree T produced by breadth-first traversal are the shortest paths from the root y to all other vertices in T.

Solution

The definition of tree itself means that there is only one possible path between any two vertices. So that path will be shortest. Breadth first traversal will produce a produce a path from root to all nodes. As there is only one possible path ina a tree, that path will be the shortest.