循环群上有向Cayley图的Hamilton圈

摘要

G是一个有限群, M是G的一个极小生成集. 用Cay(M∶G)表示生成集为M的G上的一个Cayley图, Zn表示模n的剩余类加群. 研究Zn上的有向Cayley图的Hamilton圈的存在性,给出了有向Cayley图Cay(M∶Zn)存在Hamilton圈的若干充分条件.%The Cayley digraph of a group G with generating set M, denoted Cay(M∶G), is the digraph whose vertex set is G and whose arc set consists of an arc from g to gs whenever g∈G and s∈M. Let Zn be the additive group of integers modulo n. In this paper, the author studies the existence of Hamiltonian circuits in Cay(M∶Zn).