Math Applications

Case Study Chapter 5

Directions: Based on the data provided below, answer completely the following questions. You must show
ALL work in order to receive full credit. Your submission can be a handwritten write-up that is scanned and
submitted as a PDF or JPG file OR a typed write-up submitted as a DOC file. It must be submitted through the
original case study link. The case study is worth 60 points.
The following figure is the floor plan of an office complex. The room abbreviations are provided. The outside
hallway runs around the entire office complex but it is considered as one room. The doorways are shown on the
floor plan by the triangle shape that connects certain rooms.
1. In a graph modeling this situation, each vertex would represent a location (type of room) and each edge
would represent a door (the endpoints of each edge would be the two rooms each door connects).
a. How many vertices would be in the graph? (3 points)
b. How many edges would be in the graph? (3 points)
2. Draw the graph that models this situation. You should first draw the vertices. Each vertex needs to consist
of a clear dot with the room abbreviation labeling it. After you have the vertices drawn and labeled, then
you can insert the edges by connecting the vertices that represent the rooms that have doors connecting them
on the floorplan. Make sure your amount of vertices and edges correspond to your answer to question 1 and
to the actual amount of locations and doors shown on the floorplan. You should check this graph with Prof.
Ryczek before proceeding by texting her a picture of your graph to get approved. (14 points)
3. In the graph, are there any edges that act as bridges? Explain your answer. (4 points)
4. What are the degrees of each vertex on the graph? (14 points)
Room Abbreviations:
OH – Outside hallway
W – Waiting room
R – Reception area
P – President’s office
L – Large meeting room
H – Hallway
S1 – Storage room 1
S2 – Storage room 2
C1 – Conference room 1
C2 – Conference room 2
SO – Secretary’s office
CR – Computer room
A – Accounting
5. Is it possible to start and end in the outside hallway (OH) of the complex and walk through each door of the
complex exactly once? Explain why or why not by using appropriate theorems and referring to your graph
of the complex. (8 points)
6. Is it possible to start and end in different locations and walk through every door once in the complex?
Explain why or why not by using appropriate theorems and referring to your graph of the complex. If it is
possible, indicate what locations would be the starting and ending points. (8 points)
7. What edge would need to be duplicated on the graph in order to find an optimal eulerization of the graph?
Explain your answer. (6 points)

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