Amdm

The map below shows the layout of the city museum. The vertices represent the rooms and the edges represent the hallways. There are doors on each end of every hallway. a) Find the number of each: rooms. hallways and doors. b) Each night, the hallways are cleaned by the cleaning crew. Can you find a route that allows the cleaning crew to clean each hallway exactly once? What process would be better (Euler Path, Euler Circuit. Hamilton Path. Hamilton Circuit)? If you found a route. what was it? c) The security guard is supposed to monitor each room at specific times of the night. He is supposed to start/ end at Vertex B.. Can you find a route that allows the guard to monitor each room exactly once fall the hallways do not have to be monitored)? What process would be better (Euler Path, Euler Circuit. Hamilton Path Hamilton Circuit)? If you found a route. what was it What is the Chromatic number of the graph? (Provide an answer and explain. What vertices would be what color? To receive full credit, you MUST provide answers and EXPLAIN your process