A group of Canadian friends is planning a road trip to explore cities across the United States in the summer. They want to ensure that they will only visit each city once and return to their starting point without backtracking. They came together and created a map (Figure 1) for their trip, with all roads between the cities they were planning to visit. The cities are represented as vertices, and the roads connect them as edges. a) Determine whether the graph they came up with is an Eulerian graph and explain why or why not. b) Also, determine if the graph is a Hamiltonian graph. If it is, provide the Hamiltonian cycle. Miami Denver Chicago Seattle Dallas Houston Figure 1: Trip Map