# Unit 2 – Individual Project

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

**30 %**discount on an order above

**$ 100**

Use the following coupon code:

RESEARCH