B (E Find the total number of spanning trees with free diagram.

[Problem 9] Starting at vertex A, run Prim's algorithm on the following graph. You do not need to draw all steps but you must display the final picture of the generated minimum spanning tree and the order of inclusion of edges into the tree, using standard notation (u,v) to represent an edge between hypothetical vertices u and v, in order to receive points. B A 1 2 D 3 F

[Note: Assume height of leaf node = 0 and height of root node = h. For (a) and (b), you need to explain the number of nodes at each level of the binary tree. For answering part (c), use the results in (a) and (b)]

2. Trees. i. For the graph pictured below, use the Matrix Tree Theorem to compute the number of labeled spanning trees. Write complete sentences, show all of your work, make your reasoning clear, and do not leave out any details. (a) ii. Draw all of the distinct labeled spanning trees of the graph pictured above.