Decomposition of Augmented Cubes into Regular Connected Pancyclic Subgraphs
Abstract
In this paper, we consider the problem of decomposing the augmented cube AQn into two spanning, regular, connected and pancyclic subgraphs. We prove that for n ≥ 4 and 2n - 1 = n1 + n2 with n1, n2 ≥ 2, the augmented cube AQn can be decomposed into two spanning subgraphs H1 and H2 such that each Hi is ni-regular and ni-connected. Moreover, Hi is 4-pancyclic if ni ≥ 3.
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