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The augmented cube AQn is a variation of the hypercube Qn. This paper considers the panconnectivity of AQn (n ⩾ 3) with at most 2n−5 faulty vertices and/or edges and shows that, for any two fault-free vertices u and v with distance d in AQn, there exist fault-free uv-paths of every length from d + 2 to 2n − f − 1, where f is the number of faulty vertices in AQn. The proof is based...
As an enhancement on the hypercube Q n , the augmented cube AQ n , proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks, 40(2) (2002), 71–84], not only retains some of the favorable properties of Q n but also possesses some embedding properties that Q n does not. For example, AQ n contains cycles of all lengths from 3 to 2 ...
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