# Unit 2 – Individual Project

September 29, 2018

Complete the following in a paper of 1–2 pages:

Consider
the following graph:

.png” alt=”https://class.aiu-online.com/LCMSFileShareCommon/e13/04d/5c3/ebe/41f/8a6/e55/eef/5ea/086/37/U2IP_graph1.png”>

Complete this table by finding the degree of each
vertex, and identify whether it is even or odd:

Vertex

Degree

Even/Odd

A

B

C

D

E

F

G

H

What is the order of the graph?
Construct the 10 x 10 adjacency matrix for the graph.

The
graph below illustrates a switching network. The weights represent the
delay times, in nanoseconds, travelled by a data packet between
destinations, represented by the vertices.

.png” alt=”https://class.aiu-online.com/LCMSFileShareCommon/095/5f7/53c/339/494/7b4/3d0/669/3ca/a8a/df/U2IP_graph2.png”>
b.
Complete the following table by
finding the shortest distance and the path for that distance from vertex A to
the other vertices:

Vertex

Shortest
Distance from A

Path
from A

B

C

D

E

F

G

H

I

What is the shortest distance between A and J and the
path for that distance?

The
following graph represents a portion of the subway system of a city. The
vertices on the graph correspond to subway stations, and the edges
correspond to the rails. Your job is to write a program for a cleaning car
to efficiently clean this portion of the subway system.

.png” alt=”https://class.aiu-online.com/LCMSFileShareCommon/bf1/77c/d28/3fe/438/e9e/76f/595/bc8/539/f7/U2IP_graph3.png”>
b.
Using Euler’s theorem, explain why
it is possible to pass through all of the stations by traversing every rail
only once.
c.
Using Fleury’s algorithm, provide an
optimal path to clean all the rails by passing through them only once.
d.
Is it possible to find an optimal
path described in question 3-b that starts on any station? Explain your answer.
e.
Is it possible to find an optimal
path described in question 3-b that starts and ends at the same station?
Explain why or why not.

A network engineer lives in City A,
and his job is to inspect his company’s servers in various cities. The graph
below shows the cost (in U.S. dollars) of travelling between each city that he
has to visit.
.png” alt=”https://class.aiu-online.com/LCMSFileShareCommon/b50/c0d/e4b/63c/492/f92/262/6b6/8ea/fce/3c/U2IP_graph4.png”>
.
Find a Hamiltonian path in the
graph.
a.
Find a Hamiltonian circuit that will
allow the engineer to inspect all of the servers. How much will the cost be for
his trips?
b.
Is there another Hamiltonian circuit
that will allow the engineer to inspect all of the servers other than your
answer in question 4-b? If so, calculate the cost.

Consider the following binary tree:
.png” alt=”https://class.aiu-online.com/LCMSFileShareCommon/2a8/28c/00b/d0e/43a/1b8/3d9/778/da6/5b6/6e/U2IP_graph5.png”>
.
What is the height of the tree?
a.
What is the height of vertex H?
b.
Write the preorder traversal
representation of the tree.
c.
Write the array representation of
the tree by completing the following table:

Vertex

Left
Child

Right
Child

A

B

C

D

E

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

SEE QUESTION FILE ATTACHED BELOW

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