Year: 2025
Type: conference-paper
Abstract: We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where $K=\{1,4\}$, but we continue to extend our research to generalize for all $K$.
Author: Hilliard, Allison
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Pepperdine University
OpenAlex ID: W7018015844
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