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Many parallel and distributed algorithms have been developed using such regular data structure as linear arrays, rings, trees, and meshes on hypercube-type interconnection networks. The augmented cube AQn, proposed by Choudum and Sunitha, is a derivative of hypercubes with good geometric nature and retains all the favorable properties of the hypercube. The pancyclic properties of the n-dimensional...
For two distinct vertices u,v∈V(G), a cycle is called geodesic cycle with u and v if a shortest path of G joining u and v lies on the cycle; and a cycle C is called balanced cycle with u and v if dC(u,v)=max{dC(x,y)|x,y∈V(C)}. A graph G is pancyclic [J. Mitchem, E. Schmeichel, Pancyclic and bipancyclic graphs a survey, Graphs and applications (1982) 271–278] if it contains a cycle of every length...
In this paper, we consider the fault hamiltonicity and the fault hamiltonian connectivity of the augmented cubes AQ n . Assume that F⊆V(AQ n )∪E(AQ n ) and n⩾4. We prove that AQ n −F is hamiltonian if ∣F∣⩽2n−3 and that AQ n −F is hamiltonian connected if ∣F∣⩽2n−4. Moreover, these bounds are tight.
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