Problem 3 (20 points): There's a natural intuition that two nodes that are far apart in a communi- cation network - separated by many hops - have a more tenuous connection than two nodes that are close together. There are a number of algorithmic results that are based to some extent on differ- ent ways of making this notion precies. Here's one that involves the susceptibility of paths to the deletion of nodes. Suppose that an-node undirected graph G (V, E) contains two nodes s and t such that the distance beteween s and t is strictly greater than n/2. Show that there must exist some node v, not equal to either s or t, such that deleting v from G destroys all s- t paths. (In other words, the graph obtained from G by deleting v contains no path from s to t.) Give an algorithm with running time O(m+n) to find such a node v