1. Engineering
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Question: with explanation pls thank you...

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4 Graph Application: Network Connectivity (Adapted from Problem 9, Chapter 3 of K&T) Think of a communications network as a connected, undi- rected graph, where messages from one node s to another node t are sent along paths from s to t. Nodes can sometimes fail. If a node v fails then no messages can be sent along edges incident on v. A network is particularly vulnerable if failure of a single node v can cause two nodes, say s and t, to become disconnected That is, when v and its incident edges are removed from the network, there is no path from s to t. We call such a node v a vulnerability. 1. Suppose that connected, undirected graph G contains two nodes s and t such that the shortest path between s and t is strictly greater than n/2. Show that G must contain a vulnerability 2. Give an algorithm that, given as input G and a node s such that there is some node t for which the distance between s and t is guaranteed to be greater than n/2, finds a vulnerability. Your algorithm should have running time O(m+ n).

With explanation pls! Thank you!

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