【摘要】 设G是一个有限群,S是G的一个子集(可以含G的单位元).Bi-Cayley图BC(G,S)是一个二部图:其顶点集为G×{0,1},而边集为{{(g,0),(sg,1)}:g∈G,s∈S}.本文证明了有限交换群上连通的Bi-Cayley图BC(G,S)是Hamilton的,如果S-1=S且S含二阶元或单位元.更多还原

【Abstract】 Let $G$ be a finite group, $S$(possibly, contains the identity element) be a subset of$G$. The Bi-Cayley graph $BC(G,S)$ is a bipartite graph with vertex set $G×{0,1}$ and edge set ${{(g,0),(sg,1)}, g∈G, s∈S$. In this paper, we show that every connected Bi-Cayley graph $BC(G,S)$ on a finite abelian group is hamiltonian if $S+{-1}=S$ and $S$ contains the identity element or an element of order 2.更多还原