Let \(G\) be an undirected graph, and let \(u, v,\) and \(z\) be three nodes in the graph. Consider the problem of finding a shortest path from \(u\) to \(v\) which passes through node \(z\).

True or False: a shortest path from \(u\) to \(v\) passing through \(z\) may include node \(u\) twice.

Suppose that a breadth-first search on an undirected graph \(G\) is paused and the queue is printed. Suppose that every node in the queue is either distance 5 from the source, or distance 6. At this moment, node \(u\) is undiscovered.

True or False: it is possible that node \(u\) is distance 4 from the source.