Abstract
The Bubble-Sort graph, denoted by (n is positive integer), is a special class of Cayley graph model. In 2009, Shi and Niu [Hamiltonian decomposition of some interconnection networks, in Combinatorial Optimization and Applications, D.-Z. Du, X. Hu, and P.M. Pardalos, eds., Springer, Huangshan, 2009, pp. 231–237.] proposed the following conjecture: (i) If n is odd then is the union of edge-disjoint Hamiltonian cycles. (ii) If n is even then is the union of edge-disjoint Hamiltonian cycles and a perfect matching. In this paper, we give a construction of the decomposition of Bubble-Sort graph with n odd using the decomposition of . Moreover, if the decomposition of is given using the decomposition of then the conjecture is proved.
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