循环群半直积上Cayley图的有向Hamilton圈

Directed Hamiltonian Circuit of Cayley Graph on Semi-Direct Products of Cyclic Groups

给出了一个循环群与一个二阶循环群半直积上Cayley图存在有向Hamilton圈的一个充分必要条件，并给出了任意两个循环群半直积上Carley困存在有向Hamilton圈的一个充分条件．从而部分的解决了文献［1］中提出的问题．

D. Witte and J. A. Gallian[1]asked: when is there a directed Haniltonian circuit in the semi-direct products of cyclic groups. In this paper, a necessary and sufficient condition is presented in the case that. a cyclic group is two orders, and a sufficient condition is presented in the case that arbitrates two cyclic groups.