Hamiltonian Cycles in Cayley Graphs of Semidirect Products of Finite Groups - Lanel, G. H. J; Jinasena, T. M. K. K; Welihinda, B. A. K (European Modern Studies Journal, 2020)
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
Keywords: Cayley graph, connected and bridgeless, finite groups, Hamilton cycle, perfect matching, semidirect product, standard generating set