Abstract:The n-dimensional augmented cube AQ n is a variation of the hypercube Q n : It is a ð2n À 1Þ-regular and ð2n À 1Þ-connected graph on 2 n vertices. One of the fundamental properties of AQ n is that it is pancyclic, that is, it contains a cycle of every length from 3 to 2 n : In this paper, we generalize this property to k-regular subgraphs for k ¼ 3 and k ¼ 4: We prove that the augmented cube AQ n with n ! 4 contains a 4-regular, 4-connected and pancyclic subgraph on l vertices if and only if 8 l 2 n : Also, we… Show more
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