A National Science Foundation (NSF) scholar, Hernandez has been exploring theoretical work with the Fibonacci number of the chorded cycle graph and finding the number of independent sets on the cycle graph.
Her original work is a first for the fields of combinatorics and graph theory. It has been presented at several professional conferences, including the Mathematical Association of America (MAA) in Birmingham, Alabama, and the STEM Innovators Conference in Savannah, Georgia.
“It’s great knowing that I am contributing work and theoretical formulas that have not yet been introduced to the mathematical community,” Hernandez said. “Graph theory is very visual, and I’m a visual learner. If I can see something, it’s usually easy for me to understand and easier to explain to people. Being able to look at the number of sets has always made things clearer for me.”A first-generation college student, Hernandez had a fondness for math applications at an early age, she explained.
“I’ve been interested in math since the 8th grade. I was good at it, so I continued to pursue it over the years. With math, I love that there is always a solution. With English, opinions always varied, but with math there was always an exact answer.”
Hernandez has received great support from Dr. Joe DeMaio, a mathematics professor at Kennesaw State and her research adviser.
“My NSF coordinator introduced me to Dr. DeMaio,” she said. “Dr. DeMaio presented the problem to our team, and it seemed really interesting. We kept working, and we were finally able to find that formula and contribute it to the math community.”
Because the research is theoretical, the applications for what Hernandez has presented are unknown but very probable for use with informational systems in the future.
“There’s not a real net when it comes to research,” Dr. DeMaio explained. “You don’t know how everything’s going to play out until it has. Nevertheless, it is always good to advance the state of knowledge in mathematics and statistics, and Denise has done that. Though we don’t know an application for her work yet, somebody will be thinking of a real, applied problem and go, ‘Wait! I can use that result.’”Hernandez seems hopeful and excited about the possibilities for her work, as well. “Graph theory, since it’s still theory, can be used in something like computer science and networking nodes. It is used a great deal in counting networks and determining which ones can be connected to others, and so on.
“The experience I’ve gained with doing this research project and the skills I’ve learned from using Icon computer programming have been amazing,” she continued. “I hope to use these skills to work with similar teams later on, in order to find results for similar projects. This is definitely a stepping stone for me to go into the math industry. The National Science Foundation has provided so many great opportunities to continue my career as a mathematician. I’m very blessed that this organization believes in me and is willing to invest in me and my work.”
