Term of Award

Spring 2015

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Mathematical Sciences

Committee Chair

Colton Magnant

Committee Member 1

Jonathan Hilpert

Committee Member 2

Hua Wang


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.