Presentation Type
Poster
Presentation Type
Submission
Keywords
Hamiltonian cycles, circulant graphs, counting, digraph, winding number, generating function, edges, and circuit
Department
Mathematics
Major
Mathematics
Abstract
We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.
Faculty Mentor
Joshua Bowman
Funding Source or Research Program
Academic Year Undergraduate Research Initiative, Summer Undergraduate Research Program
Location
Waves Cafeteria
Start Date
11-4-2025 1:00 PM
End Date
11-4-2025 2:00 PM
Counting Hamiltonian cycles in quartic circulant graphs
Waves Cafeteria
We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.
