Dave Witte Morris
Published 2013-06-23Version 1
We construct an infinite family of connected, 2-generated Cayley digraphs Cay(G;a,b) that do not have hamiltonian paths, such that the orders of the generators a and b are arbitrarily large. We also prove that if G is any finite group with |[G,G]| < 4, then every connected Cayley digraph on G has a hamiltonian path (but the conclusion does not always hold when |[G,G]| = 4 or 5).
Comments: 10 pages, plus 14-page appendix of notes to aid the referee
2-generated Cayley digraphs on nilpotent groups have hamiltonian paths
On a New Graph defined on the order of elements of a Finite Group
On the connectivity of enhanced power graph of finite group
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