September 28, 2025Open Access

Edge pancyclic Cayley graphs on symmetric group

Key Points

The derangement graph $Γ_n$ is edge pancyclic for $n 8 4$, representing a significant advancement or finding in graph theory.
Cayley graphs are established to be Hamiltonian and Hamilton-connected, providing structural insights into their properties.
By extending results to other classes of Cayley graphs, the work broadens the understanding of these structures within symmetric groups.
This research highlights the interconnectedness of Cayley graphs and derangement graphs, reinforcing the significance of these findings.

Abstract

We study the derangement graph Γₙ whose vertex set consists of all permutations of \1, , n\, where two vertices are adjacent if and only if their corresponding permutations differ at every position. It is well-known that Γₙ is a Cayley graph, Hamiltonian and Hamilton-connected. In this paper, we prove that for n 4, the derangement graph Γₙ is edge pancyclic. Moreover, we extend this result to two broader classes of Cayley graphs defined on symmetric group.

Edge pancyclic Cayley graphs on symmetric group

Key Points

Abstract

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