Graduate STEM Fellow Profile

Samantha Graffeo

Project Title: Transforming Experiences
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.
Teaching Partner(s):

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 K√∂nigsberg 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.