Question: (a) Define a Minimum Spanning Tree (MST) for a weighted undirected graph. (4 marks) (b) Briefly describe Prim's algorithm for finding an MST. (6 marks)

(a) Define a Minimum Spanning Tree (MST) for a weighted undirected

(a) Define a Minimum Spanning Tree (MST) for a weighted undirected graph. (4 marks) (b) Briefly describe Prim's algorithm for finding an MST. (6 marks) (c) Give an argument that Prim's algorithm is correct, i.e. that it will always find an MST. Hint: consider partitioning the nodes into two sets V1 and V2 and consider the edges between them. (5 marks) (d) Suppose that all the weights on the graph are different. I.e. that no two edges have the same weight. In this case argue that the MST is unique. Hint: consider the partition used in part c

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