3 The network below shows vertices \(A , B , C , D\) and \(E\). The number on each edge shows the distance between vertices.
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- In the case where \(x = 8\), use Kruskal's algorithm to find a minimum spanning tree for the network. Write down the order in which you add edges to your minimum spanning tree.
- Draw your minimum spanning tree.
- Write down the length of your minimum spanning tree.
- Alice draws the same network but changes the value of \(x\). She correctly uses Kruskal's algorithm and edge \(C D\) is included in her minimum spanning tree.
- Explain why \(x\) cannot be equal to 7 .
- Write down an inequality for \(x\).