Abstract: Modified bubble sort networks arc important cayley graphs model in networks design. One variety conjectures of modified bubble sort networks were proposed as follows : for any integer n>=3 , modified bubble sort networks Y are a union of i edgcdisjoint hamiltonian cycles and n一2i perfect matchings of Y，and 1<=i.We proved the conjec到lures are true for i=1，2.

Key words: Cayley graph, Modified bubble sort network, Hamiltonian cycle