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This is a Quantitative Study study.

October 16, 2025Open Access

Symmetry classes of Hamiltonian cycles

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Cayley graphs of abelian groups are not hamiltonian-transitive, showing at least two distinct hamiltonian cycles.
Hamiltonian-transitivity relates to the prime factors of a cartesian product decomposition in graphs.
The study constructs infinite families of regular hamiltonian-transitive graphs, showcasing structural properties.
By exploring both hamiltonian-transitive and non-transitive cases, the findings extend the understanding of graph symmetries.

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This research reveals properties of hamiltonian cycles in graphs, indicating structures in hamiltonian-transitive cases.

Baligacs et al. (2025) studied this question.

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