Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian

2015/07/17 by Dave Witte Morris, Morris, Dave Witte
Mathematics · #05C25 #05C45 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C25 #msc:05C45

paper · pdf · doi:10.48550/arxiv.1507.04973

7 pages, plus a 22-page appendix of notes to aid the referee

arxiv created 2015/07/17 · arxiv updated 2015/07/20

Abstract

This note shows 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, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian cycle in every connected Cayley graph on the direct product of the cyclic group of order p with the alternating group A₅ on five letters.

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