Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian
Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian
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,
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- Başlangıç: 2015
- Yayıncı: İrfan ŞİAP
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Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian