Abstract
The bubble-sort graph is an important interconnection network designed from Cayley graph model. One conjecture is proposed in Shi and Lu (2008) [10] as follows: for any integer n ⩾ 2 , if n is odd then bubble-sort graph B n is a union of n − 1 2 edge-disjoint hamiltonian cycles; if n is even then bubble-sort graph B n is a union of n − 2 2 edge-disjoint hamiltonian cycles and its perfect matching that has no edges in common with the hamiltonian cycles. In this paper, we prove that conjecture is true for n = 5 , 6 .
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