3 The diagram shows a network. The weights on the arcs represent distances in miles. The direct path between any two adjacent vertices is never longer than any indirect path.
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1. By deleting vertex \(U\) and all arcs connected to \(U\), find a lower bound for the length of the shortest cycle that visits every vertex of this network.
2. Find a vertex that can be used as the start vertex for the nearest neighbour method to give a cycle that passes through every vertex of this network. Give your cycle and its length.