Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian

Year 2016, Volume: 3 Issue: 1, 13 - 30, 11.01.2016

Dave Witte Morris

https://doi.org/10.13069/jacodesmath.66457

Abstract

We show there are infinitely many finite groups~$G$, such that every connected Cayley graph on~$G$ has a hamiltonian cycle, and $G$ is not solvable. Specifically, we show that if $A_5$~is the alternating group on five letters, and $p$~is any prime, such that $p \equiv 1 \pmod{30}$, then every connected Cayley graph on the direct product $A_5 \times \integer _p$ has a hamiltonian cycle.

Keywords

Cayley graph, Hamiltonian cycle, Solvable group, Alternating group

References

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