Graduate STEM Fellow Profile
Thesis: Graph labeling using quasi-groups and extending results of the Path Partition Conjecture
College/University: University of Colorado Denver
Research Advisor: Michael Jacobsen
Degree Sought: Ph.D. Applied Mathematics, Graph Theory
Department: Mathematical and Statistical Sciences
Research Focus: Predominantly focuses on the labeling and structural properties of graphs.
Description of Research
I extend the use of integers and addition used in the study of sum graphs to that of quasi-group representations of graphs. I find graph labelings using the fewest elements possible without the need to add additional isolates to the original graph. Beyond this, I extend the results supporting the Path Partition Conjecture to include graphs that are tripartite, a result I hope to extend further.
Example of how my research is integrated into my GK-12 experience
One example integrating my research is the “Question of the Week” that I often ask my classes. Each week I present a challenge question to my students that hopefully gets them thinking in ways that they have not done before. Often these questions are classics from graph theory–the Königsberg Bridge Problem, or the three houses and three utilities–but sometimes they are simply challenging mathematical questions that get the students thinking on a higher level.