1. Give an example of a (simple, undirected) graph G = (V, E), a start vertex s V and a set of tree edges ET E such that for each vertex v V , the unique path in the graph (V, ET ) from s to v is a shortest path in G, yet the set of edges ET cannot be produced by running a breadth-first search on G, no matter how the vertices are ordered. Include an explanation of why your example satisfies the requirements.

1. Give an example of a simple, undirected) graph G = (V, E), a start vertex s EV and a set of tree edges ET CE such that for each vertex v EV, the unique path in the graph (V, ET) from s to v is a shortest path in G, yet the set of edges Et cannot be produced by running a breadth-first search on G, no matter how the vertices are ordered. Include an explanation of why your example satisfies the requirements