<p> Discrete Math Graph Coloring Project 1. Find your fellow group members. 2. Create a map for a fictional country (minimum 8 regions, maximum 12). Draw your country (NEATLY) on a piece of white computer paper. DO NOT color the map, simply sketch it and label all of its regions. Be sure that your group members’ names are all on the paper. 3. Receive another group’s map from your teacher. 4. Once you’ve received the new map, construct a connected graph that represents it on a separate sheet of white computer paper. 5. Determine the graph’s chromatic number by coloring the graph. Then, color the corresponding map based on your work. 6. On the same sheet of paper as you drew your graph, answer the following questions: a. Will your graph have an Euler path, an Euler circuit, or neither? Explain your answer. If the graph has a path or a circuit, list it. b. Will your graph have a Hamiltonian circuit? If it does, list the circuit and if does not, explain why. c. Is your graph a multi-graph? Explain why or why not. d. Construct an adjacency matrix to represent your graph. What are the sums of all of the rows and columns of the matrix? In terms of this problem, what do these sums represent? 7. Now, take a glue stick and glue both pieces of paper to one piece of construction paper (The map you received and your groups work). BE SURE to put your group members’ names on the construction paper when you’re done. 8. When your group is finished and ALL of your materials are put away, you can begin to work on your take-home test for Chapter 4 together. </p>