Question 4: Suppose you had a road network represented as a connected graph (vertices are intersections and edges are roads between intersections). How can you determine if closing a set of intersections results in the inability to travel between some remaining pair of intersections? Note: If an intersection is closed, all edges touching that vertex are closed too. You may assume we already know about depth first search, breadth first search, minimum spanning tree algorithms, and the shortest path algorithm from class, but you can’t assume anything else from class.

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.