Applications of Discrete Mathematics

Project description
Task Background: Graphs and Trees are useful in visualizing data and the relations within and
between data
sets. Conversely, it is also important to be able to represent graphs as databases or arrays, so
that programs for processing the data can be written.

Part I: Adjacency Matrix and Shortest Path

Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices
consistent with the placement of numbers within the matrix.

10 6 0 5 0l

| 6 0 1 0 3 |

| 0 1 0 4 8 |

| 5 0 4 0 0 |

L0 3 8 0 0J
Describe the graph and why it is consistent with the matrix.
How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those
paths?
Part II: Trees
Construct and describe a tree that indicates the following: A college president has 2 employees who
answer directly to him or her, namely a vice president and provost. The vice president and provost
each have an administrative assistant. Three deans answer to the provost, and the heads of finance
and alumni relations answer to the vice president. Each dean oversees three department
chairpersons, and each department chair oversees several faculty in each of their respective
departments.
Suppose that the professional correspondences are the same as above, with the addition that there
is also a direct working relationship between the college president and the head of alumni
relations (it is
not necessary to draw this). Would the graph still be a tree? Why or why not?

Task Type:
Individual Project
Deliverable Length:
2 Parts: See Assignment Details
Points Possible:
100
Due Date:
6/9/2014 11:59:59 PM CT
Weekly tasks or assignments (Individual or Group Projects) will be due
by
Monday and late submissions will be
assigned a late penalty in accordance with the late
penalty policy found in the syllabus. NOTE: All submission
posting times are based on midnight Central Time.
Task Background:
Graphs and Trees are useful in visualizing da
ta and the relations wi
thin and between data
sets. Conversely, it is also important to be able to re
present graphs as databases or arrays, so that programs
for processing the data can be written.
Part I: Adjacency Matrix and Shortest Path
Construct a graph based on the adjacency matrix that
appears below. Label all nodes with indices consistent
with the placement of numbers within the matrix.
G
0 6050
?
|
6 0103
|
|
0 1048
|
|
5 0400
|
?
0 3800
?
Describe the graph and why it is consistent with the matrix.
How many simple paths are there from vertex 1 to
vertex 5? Explain.Which is the shortest of those
paths?
Part II: Trees
Construct and describe a tree that indicates the fo
llowing: A college president has 2 employees who
answer directly to him or her, namely a vice president and provost. The vice president and provost
each have an administrative assistant. Three dean
s answer to the provost, and the heads of finance
and alumni relations answer to the vice pres
ident. Each dean oversees three department
chairpersons, and each department chair oversees several faculty in each of their respective
departments.
Suppose that the professional correspondences are th
e same as above, with the addition that there is
also a direct working relationship between the college
president and the head of alumni relations (it is
not necessary to draw this). Would the graph still be a tree? Why or why not?
Please submit your assignment.
Click on
Student Expectations
to view the expectations for this assignment.
For assistance with your assignment, please use your text, Web resources, and all course materials.
Course Materials
Phase Resources:
Breadth-first search
Breadth-first search defined. Page also contains links
to Depth-first search, best-first search, and other data
structures terms. Paul E. Black, “breadth-first search
“, in Dictionary of Algorithms and Data Structures
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