Strategies and Algorithms towards the pebbling number of Lemke x Lemke

Nancy Villegas Sanchez, Miguel Solis, Erika Lopez, Susan Phillips, & Dr. Jorge Garcia


In this poster presentation, faculty advisor Jorge Garcia (Mathematics) and his group of students will present on strategies and algorithms that target a specific vertex of a specific pebbled graph, Lemke x Lemke. These strategies will contribute to solve an old problem in Graph Theory known as Graham’s Conjecture. The strategies include theorems and meta-theorems that help us better understand the graph. We wish to contribute to Graham’s Conjecture and organize the data. We will be using Maple to organize these theorems and solutions. This program is helping us organize and finalize the information that we gain throughout our search. We will be including solutions that exists and do not exist into the theorem to make better sense of the information that we have gained over the past couple of weeks. Overall, we hope to shine light on Graham’s Conjecture and provide any contributions or theorems that may better the conjecture.


Session 2

3:00pm – 4:30pm

Grand Salon


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