ยง Big list of questions on the structure of graphs

I've been trying to get more of a feeling for graphs lately, so I'm collecting sources of "structural" questions of graphs and answers for these questions.
Q. Is it possible in an unweighted graph, there is exactly one unique shortest path tree for a node u but more than one such shortest path tree for some other node v ?
Q. Can I orient the edges of a bridge-less undirected bipartite graph with even no. of nodes such that all the nodes are in a cycle ?