Display the resulting Minimum Spanning Tree $($MST$)$ given by Prim's Algorithm. For Prim's algorithm, initiate your cloud at Boston.

Give the Hamiltonian cycle generated by the MST algorithm as discussed in class. When illustrating your tree, ensure that within each level of the tree, the order of the nodes from left to right corresponds to the sequence in which they were added to the cloud during Prim's algorithm.

Given your result from $3,$ provide a lower bound on the optimal solution to TSP on the graph. You should infer the lower bound using a property of the MST algorithm.