摘要
设Ｘ是有限群Ｇ的一个生成集．Ｃａｙ（Ｘ：Ｇ）表示生成集为Ｘ的Ｇ上的Ｃａｒｌｅｙ图，其顶点集为Ｇ，其边集为所有无序对［ａ，ｂ］组成的集合，其中ａ，ｂ∈Ｇ，ａ－１ｂ∈Ｘ∪Ｘ－１（Ｘ－１＝｛ｘ－１｜ｘ∈Ｘ｝）．若图的每条边都在的Ｈａｍｉｌｔｏｎ圈上，则称图是边－Ｈａｍｉｌｔｏｎ图．本文证明了：当Ｇ为ｐ－群或Ｈａｍｉｌｔｏｎ群时，若Ｘ含有Ｇ的中心元，则Ｃａｙ（Ｘ：Ｇ）是边－Ｈａｍｉｌｔｏｎ图．
Let X generate the finite group G. A Cayley graph of generators X over G is defined as a graph Cab(X: G) whose vertex set is G and whose edge set consists of all unordered pairs [a, b] with a, b ∈ G and a-1 b∈ E X U X-1, where X-1 = {x-1|x∈ X}. We say that Cab(X: G) is edge-Hamiltonian if every edge lies on a Hamilton cycle of Cab(X: G). Let Z(G) be the center of G. In this note, we study the edge-Hamiltonian property of Cab(X: G).The main results are two theorems: 1) If G is a p-group and Z(G) ∩ X ≠ 0, then Cay(X: G)is edge-Hamiltonian. 2) If G is a Handltonian group and Z(G) ∩ X ≠ 0, then Cay(X: G) is edge-Hamiltonian.
出处
《系统科学与数学》
CSCD
北大核心
1995年第3期266-268,共3页
Journal of Systems Science and Mathematical Sciences
