Find a Hamilton circuit that begins with the vertices F, B and + ends with the vertices A, F. F D A C B E G . . . G A C D E B F Drag each of the vertices given above into the area below to create a Hamilton circuit.Complete the following for the graph on the right. 4 C E F a. Determine if the graph must have Hamilton circuits. ok T 1 g b. If the graph must have Hamilton circuits, determine the number of such circuits. - T 7_ K L a. Must the graph have Hamilton circuits? () A. No, it might not because it is complete and has at least three vertices. () B. Yes, it must because it is complete and has at least three vertices. C. Yes, it must because it is not complete. D. No, it might not because it is not complete. b. How many circuits, if any, does the graph have? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The graph has | | Hamilton circuits. () B. The graph does not have any Hamilton circuits. Use the complete, weighted graph on the right, to find the total weight of the following Hamilton circuit. A B,E C,D A The total weight of the Hamilton circuit is |:| You have five errands to run around town in no particular order. You must visit the post office (P), bank (B), dry cleaners (D), hospital (H), and market (M). A weighted graph is shown with the distances (in miles) to the locations shown on the edges. Using the Brute Force Method, one optimal solution is home, market, post office, dry cleaners, hospital, bank, and home. What is the total length of this shortest route? The total length of the shortest route is miles. You have five errands to run around town in no particular order. You must visit the post office (P), bank (B), dry cleaners (D), hospital (H), and market (M). A weighted graph is shown with the distances (in miles) to the locations shown on the edges. Use the Nearest Neighbor Method to find an approximate solution. What is the total length of the shortest route using this solution? How does this compare to the shortest route from the Brute Force Method? Use the Nearest Neighbor Method to find an approximate solution. hospital | dry cleaners | post office | market | home || bank Drag each of the vertices given above into the area below to determine the correct circuit. Using the Brute Force Method, one optimal solution is home, market, hospital, bank, dry cleaners, post office, and home. How does the length of the route found above compare to this solution? Select the correct choice below and fill in the answer box(es) to complete your choice. (Type a whole number.) O A. The distance found using the Nearest Neighbor Method is shorter than the distance using the Brute Force Method. Using the Nearest Neighbor Method, the distance is miles and using the Brute Force Method, the distance is miles. (U B. The distance found using the Nearest Neighbor Method is longer than the distance using the Brute Force Method. Using the Nearest Neighbor Method, the distance is miles and using the Brute Force Method, the distance is miles. O C. The distances are both | | miles. Determine whether the graph is a tree. If the graph is not a tree, give the reason why. H D The graph is a tree. The graph is not a tree because it is disconnected. The graph is not a tree because it has one or more circuits. Find a spanning tree for the connected graph. Choose the correct answer below. C F Use Kruskal's Algorithm to find the minimum spanning tree for the weighted graph. Give the total weight of the minimum spanning tree. Which of the following trees matches the shape of the minimum spanning tree? O A. O B. o Lo L) What is the total weight of the minimum spanning tree? The total weight is |: \" A college campus plans to provide awnings above its sidewalks to shelter students from the rain as they walk from the parking lot and between buildings. To save money, awnings will not be placed over all of the sidewalks shown in the figure. Just enough awnings will be placed over a select number of sidewalks to ensure that students walking from building to building will be able to do so without getting wet. Complete parts (a) and (b) below. ) Click here to view the campus map. a. Use a weighted graph to model the given map. Represent buildings as vertices, sidewalks as edges, and sidewalk lengths as weights. Select the correct graph below. 1 2 155 60 \\92 b. Use Kruskal's Algorithm to find a minimum spanning tree that allows students to move between the parking lot and any building without getting wet. What is the total length of the sidewalks that need to be sheltered by awnings? Select the correct minimum spanning tree below. o 136 124 136 O B. 124 11\\ 36 1 36 m 75 75 60 \\92 60 \\ 92 60 \\ o2 The total length of the sidewalks that need to be sheltered is feet. The graph shows a proposed layout of a bike trail system to be installed between the towns shown. The vertices represent the ten towns, designated A through J. The edges indicate all possible choices for building the trail. The weights show the distances, in miles, between bike trailheads connecting towns. Use Kruskal's Algorithm to determine the minimum mileage for the bike trail and layout of the trail system. ) Click the icon to view the bike trail system. Identify the minimum spanning tree of the given graph. A The minimum mileage for the bike trail is miles