【摘要】 对于以一个旋转和两个反射为生成元集的二面体群D_q,本文证明了W。Holsztyn′ski和R.F.E.Strube提出的猜想,本文还给出循环群Z₂ⁿ上Cayley图Hamilton分解的一个充分条件更多还原

【Abstract】 This paper gives sufficient conditions for Hamiltonian decomposition of Cayley graphs on the cyclic group of order 2" and on the dihedral group of order 2q.If S =-{s1,s1-,s2,s2-1} is a generating set for a cyclic group Z2n of order 2n and o(s1)=o(s2) = 2n s2∈ {s1,s1-1}, then Cay(Z2" ;S) can be decomposed into Hamiltonian cycles. And for a dihedral gorup Dq of order 2q, if S = {s1;s1-1,s2 = s2-1,s3 = s3-1} is a generating set for Dq, o(s1) = q,o(s2)=2, Ss = s2s1-1, then Cay(Dq;S) can also be decomposed into Hamiltonian cycles.更多还原