Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In...Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In this paper, we first provide two interesting results for edge-hamiltonian property of Cayley graphs and bi-Cayley graphs. Next, we investigate the edge^hamiltonian property of F = BCay（G, S）, and prove that F is hamiltonian if and only if F is edge-hamiltonian when F is a connected bi-Cayley graph.展开更多
基金partially supported by the NSFC(No.11171368)the Scientific Research Foundation for Ph.D of Henan Normal University(No.qd14143 and No.qd14142)
文摘Let G be a finite group, and S be a subset of G. The bi-Cayley graph BCay（G, S） of G with respect to S is defined as the bipartite graph with vertex set G x {0,1} and edge set {（g,0）, （gs, 1）1 g ε G, s εS}. In this paper, we first provide two interesting results for edge-hamiltonian property of Cayley graphs and bi-Cayley graphs. Next, we investigate the edge^hamiltonian property of F = BCay（G, S）, and prove that F is hamiltonian if and only if F is edge-hamiltonian when F is a connected bi-Cayley graph.
