The diagram above represents a graph. Use the following abbreviations to represent the nodes: MH= Mayors house; BA= Bakery; MF= McFanes's Farm; BR= Brewery; TF= Thomas' Farm; IN=In; DC= Dry cleaner; LI=Library and CH= City Hall (a) Using either adjacency matrix or list, what is the time complexity of adding a new facility, say School (SC). The community has decided to remove either the Brewery or Inn. What is the time complexity of doing this? (b) The following roads are unidirectional (one-way): MF-> BR=21, DC->IN= 19, LI->IN=6, MF->BA= 9; IN->BR=5, what is the complete adjacency matrix? All roads leading to the Mayor's house are one-way and 17 miles each. Other non-given roads are 12 miles in length (bidirectional). (c) Produce the adjacency list and state whether the graph is dense, sparse and/or planar. Justify your answer. Bakery Mayor's House McFane's Farm Brewery Inn Library Thomas Farm Dry cleaner City Hall