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The bubble-sort star graph is an interconnection network for multiprocessor systems. Recursive structure is important for interconnection networks, since it can reduce the complex cases into simple cases, and it can keep good properties independent of dimensions. Many algorithms use the idea of recursive construction. Edge-disjoint Hamiltonian cycles not only provide the basis of all-to-all broadcasting algorithm for networks but also provide a replaceable Hamiltonian cycle for transmission when the other Hamiltonian cycle contains faulty edges in an interconnection network. In this paper, we propose the recursive definition of bubble-sort star graphs. Then as an application, we obtain two edge-disjoint Hamiltonian cycles of bubble-sort star graphs.

Recursive definition and two edge-disjoint Hamiltonian cycles of bubble-sort star graphs