Abstract:
It has been conjectured that every connected Cayley graph of order greater
than has a Hamilton cycle. In this paper, we prove that the Cayley graph of
with respect to a generating set , , where with
and is Hamiltonian for . Furthermore, the existence of a Hamilton cycle in
the Cayley graph of a semidirect product of finite groups is proved by placing restrictions on
the generating sets. Consequently, the existence of a Hamilton cycle in the Cayley graphs of
several isomorphism types of groups of orders
and
, where is also
proved
