## Abstract

In this paper, we investigate the existence of a hamiltonian circuit in the cartesian product of two Cayley digraphs. Three of our results can be summarized as follows. Suppose K is the Cayley digraph of a dihedral, semidihedral, or dicyclic group arising from a specified pair of (standard) generators, and suppose L is a Cayley digraph with a hamiltonian circuit. Then, the cartesian product of K and L has a hamiltonian circuit. As a corollary to our main theorem, we also show that the cartesian product of an undirected cycle of length n and a directed cycle of length k has a hamiltonian circuit unless n = 2 and k is odd. Some open problems are stated.

Original language | English (US) |
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Pages (from-to) | 297-307 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 43 |

Issue number | 2-3 |

DOIs | |

State | Published - 1983 |

### Bibliographical note

Funding Information:One of the authors( G.L.) did her work at the Universityo f MinnesotaD, uluth, while in an UndergraduatRe esearchP articipationp rogramf undedb y the National ScienceF oundation( Grant NumberN SF/SPI-7926564).