Hamiltonian Cycles in Cayley Graphs of Semidirect Products of Finite Groups

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