Hamiltonicity of Transitive Graphs Whose Automorphism Group Has \Z_p as Commutator Subgroups

2024/12/11 by Florian Lehner, Farzad Maghsoudi, Lehner, Florian +3
Computer Science · Mathematics · #05C25 #05C45 #05C63 #20E06 #20F05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2412.08105

openalex publication_date 2024/12/11 · openalex created_date 2024/12/13 · openalex updated_date 2026/07/28

Abstract

In 1982, Durnberger proved that every connected Cayley graph of a finite group with a commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend this result to the infinite case. Additionally, we generalize this result to a broader class of infinite graphs X, where the automorphism group of X contains a transitive subgroup G with a cyclic commutator subgroup of prime order.

Related

• Automorphism groups with cyclic commutator subgroup and Hamilton cycles
• Cayley graphs on groups with commutator subgroup of order 2p are hamiltonian
• Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian
• Symmetry classes of Hamiltonian cycles
• Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian