两类可解群双Cayley图的Hamilton性

Hamiltonian Property in Bi-Cayley Graphs of Two Kinds of Finite Solvable Groups

该文研究双Cayley图Γ∶=BCay(G,S)的Hamilton性.通过Γ所对应的(单)Cayley图,G的商群的双Cayley图,乃至Γ的导出子图的Hamilton圈来构造Γ的Hamilton圈.获得了关于pq阶群(其中p>q>2是素数)和广义四元数群Q4r(r为奇素数)双Cayley图Hamilton性的一些结果.

For a bi-Cayley graphΓ∶=BCay(G,S),its Hamiltonian property is researched in this paper,and its Hamiltonian cycles are constructed by those Hamiltonian cycles of the corresponded(single)Cayley graph,of the bi-Cayley graph on G’s quotient group,and of its induced subgraphs.Furthermore,some results about the Hamiltonian property of bi-Cayley graphs on the group which has order pq(p>q>2 are prime)or on the generalized quaternion group Q4r(r is odd prime)are obtained.