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One of the important issues in evaluating an interconnection network is to study the Hamiltonian cycle embedding problems. For a positive integer  k , a graph  G  is said to be  spanning  k -cyclable  if for  k  prescribed vertices, there exist  k  disjoint cyclessuch that the union ofspans  G , and eachcontains exactly one vertexof. According to the definition, the problem of finding hamiltonian cycle focuses on  k  = 1. The notion of spanning cyclability can be applied to the problem of identifying faulty processors and other related issues in interconnection networks. The  n -dimensional augmented cubeis an important node-symmetric variant of the  n -dimensional hypercube. In this paper, we prove thatwithis spanning  k -cyclable for.

Embedding spanning disjoint cycles in augmented cube networks with prescribed vertices in each cycle