Physical Sciences and Mathematics Commons^™

Edge Colorings Of Graphs And Their Applications, Daniel Johnston

Dissertations

Edge colorings have appeared in a variety of contexts in graph theory. In this work, we study problems occurring in three separate settings of edge colorings.

For more than a quarter century, edge colorings have been studied that induce vertex colorings in some manner. One research topic we investigate concerns edge colorings belonging to this class of problems. By a twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of …

Graphs Of Classroom Networks, Rebecca Holliday

Electronic Theses and Dissertations

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 …