HW 16: Trees (22 points) MIS Graph Theory 24, S1, S2, S3, S4, S5 24. (5 points) The graph below (copied twice) shows the costs, in thousands of dollars, to lay fiber optic cables between pairs of buildings. a) Use Kruskal’s algorithm to find a minimal spanning tree for the graph. List the order in which you add the edges. What is the total cost? b) Use Prim’s algorithm starting with vertex A to find a minimal spanning tree. List the order in which you add the edges. S1. (3 points) Find all possible spanning trees for the graph (draw them separately). S2. (1 point) Find a spanning tree for the graph (you can draw the tree right on the graph). S3. (2 points) Use Kruskal’s algorithm to find a minimal spanning tree for the graph. List the order in which you add the edges. S4. (3 points) Use Prim’s algorithm starting with vertex a to find a minimal spanning tree. List the order in which you add the edges. S5. (8 points) For each description below, either draw a graph meeting the criteria, or explain why one doesn’t exist. a) Tree, 9 vertices, 9 edges b) Graph, connected, 9 vertices, 9 edges c) Graph, circuit-free, 9 vertices, 6 edges d) Tree, 5 vertices, total degree 8