Hamiltonian Cycles in Circulant Quartic Graphs

Author(s)

John PalmerFollow

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

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Mar 24th, 2:00 PM Mar 24th, 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.