Q 3 The graph in figure 1 is a sales network, where • s represents a factory producing pop-its, ⚫t is the local school, - • other vertices (a – f) are agents onselling pop-its. edges represent sales connections S t A radical group wants to stop pop-its reaching the local school by disrupting sales. f Figure 1: Graph to disconnect (a) What is the minimum number of connections whose deletion would stop pop-its reaching the local school? (b) A marketing expert claims that network is 3-edge connected between s and t, explain why they are mistaken. (c) We can translate the network into a network by attaching directions to each edge. (i) If we ignore that we want s to be the source and t to be the sink, then how many orientations can we put on the graph? (ii) We do wants to be the source and t to be the sink of a network. How many networks can we setup? (iii) For the network in figure 2 (with the given intial flow), use Ford-Fulkerson to show it is a maximum flow, identify the min-cut, and explain why this result implies the original graph is at least 2-edge connected from s to t. 1,1 a d 1,1 1,0 1,0 1,1 1,1 1,1 S b t 1,1 1,0 1,0 с f 1,1 Figure 2: Graph with flow

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