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The hypercube family Q n is one of the most well-known interconnection networks in parallel computers. With Q n , dual-cube networks, denoted by DC n , was introduced and shown to be a (n + 1)-regular, vertex symmetric graph with some fault-tolerant Hamiltonian properties. In addition, DC n 's are shown to be superior to Q n 's in many aspects. In this article, we will prove that the n-dimensional dual-cube DC n contains n + 1 mutually independent Hamiltonian cycles for n ≥ 2. More specifically, let v i ∈ V (DC n ) for 0 ≤ i ≤ |V (DC n )| − 1 and let v 0 , v 1 , . . . , v |V (DC n )|−1 , v 0 be a Hamiltonian cycle of DC n . We prove that DC n contains n +1 Hamiltonian cycles of the form v 0 , v k 1 , . . . , v k |V (DC n )|−1 , v 0 for 0 ≤ k ≤ n, in which v k i = v k i whenever k = k . The result is optimal since each vertex of DC n has only n + 1 neighbors.

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