Hamiltonian Cycles in Circulant Quartic Graphs
Presentation Type
Poster
Presentation Type
Submission
Keywords
Graph Theory, Combinatorics, Topology, Winding Number, Generating Functions, Integer Sequences, Fibonacci Numbers, Cycles, Paths, Torus
Department
Mathematics
Major
Mathematics
Abstract
We study the number of Hamiltonian cycles in two families of graphs in which each vertex has degree 4.
Within each family, we separate groups of cycles based on their "winding numbers," and we are able to calculate either explicit or recursive formulas that count cycles in each winding number category.
We then sum the respective terms from each winding number within both families to arrive at integer sequences that count the cycles.
Faculty Mentor
Joshua Bowman
Funding Source or Research Program
Academic Year Undergraduate Research Initiative
Location
Waves Cafeteria
Start Date
24-3-2023 2:00 PM
End Date
24-3-2023 4:00 PM
Hamiltonian Cycles in Circulant Quartic Graphs
Waves Cafeteria
We study the number of Hamiltonian cycles in two families of graphs in which each vertex has degree 4.
Within each family, we separate groups of cycles based on their "winding numbers," and we are able to calculate either explicit or recursive formulas that count cycles in each winding number category.
We then sum the respective terms from each winding number within both families to arrive at integer sequences that count the cycles.