Hamiltonian Cycles in Cayley Graphs of Semidirect Products of Finite Groups

  • G. H J. Lanel
  • T. M. K. K. Jinasena
  • B. A. K. Welihinda


It has been conjectured that every connected Cayley graph of order greater than 2 has a Hamilton cycle. In this paper, we prove that the Cayley graph of (Zp×Zp)⋊ Zq with respect to a generating set S, Cay((Zp×Zp)⋊ Zq, S), where S ={s,t} with |s|=p and |t|=q is Hamiltonian for p,q > 3. 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 pnq, p2q2 and p2qr, where n ≥ 2 is also proved.Key words: Cayley graph, connected and bridgeless, finite groups, Hamilton cycle, perfect matching, semidirect product, standard generating set.