Graphs of Classroom Networks

<p>In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism classes within the randomly generated graphs. Once we have reduced the problem to the isomorphism classes, we can then choose a graph we think most accurately describes the classroom network. At the end of this work, we will make a note on the rainbow connection number in oriented graphs with diameter 2.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2015

Author dc:creator

• Holliday, Rebecca

Contributors dc:contributor

• Jonathan Hilpert
• Hua Wang

• ETD
• Graphs
• isomorphism
• havel hakimi
• rainbow
• Discrete Mathematics and Combinatorics
• Other Applied Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1284

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2294