Below is the floor plan of the house of the mouse called King, where the rooms and the doors between the rooms are shown. The house is split into 7 rooms, and the passages represent the doors. T (a) Draw a graph corresponding to the floor plan above. In your graph, what do the vertices represent? When do you put an edge between vertices? (b) Is it possible for King to tour the house, passing through each doorway exactly once? If so, in which rooms must King begin and end the tour? Justify your answer. (c) King decides to add some new doors between the rooms he has. He cannot add any doors to the exterior of the house. Is it possible for cach room to have an odd number of doors? Justify your answer.