1. True or False:

a. In a complete graph, Prims algorithm has better time complexity than Kruskals algorithm for finding the MST guaranteed.

b. If a complete graph has no two edges with the same cost, the MST is guaranteed unique.

c. In a connected, undirected graph with no negative edges and unique edge costs, the shortest path between two nodes is guaranteed unique.

d. In a connected, undirected graph with no negative edges and a unique shortest path between nodes A and B, multiplying all edge costs by a positive constant C cannot change the shortest path.

e. In a connected, undirected graph with no negative edges and a unique shortest path between nodes A and B, adding a positive constant C to all edge costs cannot change the shortest path.

f. The highest cost edge in an undirected graph cannot be in the MST.

g. The least cost edge in an undirected graph must be in the MST (if it is unique).