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## Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian

#### Dave Witte MORRİS [1]

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.

Cayley graph, Hamiltonian cycle, Solvable group, Alternating group
• R. Gould, R. Roth, Cayley digraphs and (1, j, n)-sequencings of the alternating groups An, Discrete Math. 66(1-2) (1987) 91–102.
• K. Kutnar, D. Marušič, D. W. Morris, J. Morris, P. Šparl, Hamiltonian cycles in Cayley graphs whose
• order has few prime factors, Ars Math. Contemp. 5(1) (2012) 27–71.
• K. Kutnar, D. Marušič, D. W. Morris, J. Morris, P. Šparl, Cayley graphs on A5are hamiltonian, unpublished appendix to [2], http://arxiv.org/src/1009.5795/anc/A5.pdf.
• D. Witte, J. A. Gallian, A survey: Hamiltonian cycles in Cayley graphs, Discrete Math. 51(3) (1984) 293–304.
Primary Language en Articles Author: Dave Witte MORRİS Publication Date : January 11, 2016
 Bibtex @ { jacodesmath168459, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2016}, volume = {3}, pages = {13 - 30}, doi = {10.13069/jacodesmath.66457}, title = {Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian}, key = {cite}, author = {Morri̇s, Dave Witte} } APA Morri̇s, D . (2016). Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian . Journal of Algebra Combinatorics Discrete Structures and Applications , 3 (1) , 13-30 . DOI: 10.13069/jacodesmath.66457 MLA Morri̇s, D . "Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian" . Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 13-30 Chicago Morri̇s, D . "Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian". Journal of Algebra Combinatorics Discrete Structures and Applications 3 (2016 ): 13-30 RIS TY - JOUR T1 - Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian AU - Dave Witte Morri̇s Y1 - 2016 PY - 2016 N1 - doi: 10.13069/jacodesmath.66457 DO - 10.13069/jacodesmath.66457 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 13 EP - 30 VL - 3 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.66457 UR - https://doi.org/10.13069/jacodesmath.66457 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian %A Dave Witte Morri̇s %T Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian %D 2016 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 3 %N 1 %R doi: 10.13069/jacodesmath.66457 %U 10.13069/jacodesmath.66457 ISNAD Morri̇s, Dave Witte . "Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian". Journal of Algebra Combinatorics Discrete Structures and Applications 3 / 1 (January 2016): 13-30 . https://doi.org/10.13069/jacodesmath.66457 AMA Morri̇s D . Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(1): 13-30. Vancouver Morri̇s D . Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016; 3(1): 13-30.

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