On mapping parallel algorithms into parallel architectures
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Fault-tolerant Hamiltonicity of twisted cubes
Journal of Parallel and Distributed Computing
Hamilton-connectivity and cycle-embedding of the Möbius cubes
Information Processing Letters
Fault-Tolerant Embeddings of Hamiltonian Circuits in k-ary n-Cubes
SIAM Journal on Discrete Mathematics
Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures
IEEE Transactions on Parallel and Distributed Systems
ICPADS '02 Proceedings of the 9th International Conference on Parallel and Distributed Systems
Pancyclicity on Möbius cubes with maximal edge faults
Parallel Computing
Fault hamiltonicity of augmented cubes
Parallel Computing
Edge-pancyclicity of Möbius cubes
Information Processing Letters
Edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Processing Letters
Paths in Möbius cubes and crossed cubes
Information Processing Letters
IEEE Transactions on Computers
Fault-tolerant pancyclicity of augmented cubes
Information Processing Letters
Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m,4)
Theoretical Computer Science
The super connectivity of augmented cubes
Information Processing Letters
Embedding hamiltonian paths in hypercubes with a required vertex in a fixed position
Information Processing Letters
Automorphisms of augmented cubes
International Journal of Computer Mathematics
Vertex-bipancyclicity of the generalized honeycomb tori
Computers & Mathematics with Applications
Maximally Local Connectivity on Augmented Cubes
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Embedding Hamiltonian paths in augmented cubes with a required vertex in a fixed position
Computers & Mathematics with Applications
An optimal result on fault-tolerant cycle-embedding in alternating group graphs
Information Processing Letters
Conditional edge-fault Hamiltonicity of augmented cubes
Information Sciences: an International Journal
Edge-fault-tolerant vertex-pancyclicity of augmented cubes
Information Processing Letters
The panpositionable panconnectedness of augmented cubes
Information Sciences: an International Journal
Bipanconnectivity of balanced hypercubes
Computers & Mathematics with Applications
Pancyclicity of ternary n-cube networks under the conditional fault model
Information Processing Letters
Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model
SIAM Journal on Discrete Mathematics
Efficient unicast in bijective connection networks with the restricted faulty node set
Information Sciences: an International Journal
Theoretical Computer Science
Panconnectivity of Cartesian product graphs
The Journal of Supercomputing
The paths embedding of the arrangement graphs with prescribed vertices in given position
Journal of Combinatorial Optimization
Edge-fault-tolerant panconnectivity and edge-pancyclicity of the complete graph
Information Sciences: an International Journal
Two spanning disjoint paths with required length in generalized hypercubes
Theoretical Computer Science
Conditional edge-fault pancyclicity of augmented cubes
Theoretical Computer Science
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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^n, but Q"n contains only even cycles. In this paper, we obtain two stronger results by proving that AQ"n contains paths, between any two distinct vertices, of all lengths from their distance to 2^n-1; and AQ"n still contains cycles of all lengths from 3 to 2^n when any (2n-3) edges are removed from AQ"n. The latter is optimal since AQ"n is (2n-1)-regular.