A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Arrangement graphs: a class of generalized star graphs
Information Processing Letters
Cycles in the cube-connected cycles graph
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs
IEEE Transactions on Computers
Graph Theory With Applications
Graph Theory With Applications
The forwarding indices of augmented cubes
Information Processing Letters
Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes
Parallel Computing
Optimal Embeddings of Paths with Various Lengths in Twisted Cubes
IEEE Transactions on Parallel and Distributed Systems
The two-equal-disjoint path cover problem of Matching Composition Network
Information Processing Letters
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Let n and k be positive integers with n驴k驴2. The arrangement graph A n,k is recognized as an attractive interconnection networks. Let x, y, and z be three different vertices of A n,k . Let l be any integer with $d_{A_{n,k}}(\mathbf{x},\mathbf{y}) \le l \le \frac{n!}{(n-k)!}-1-d_{A_{n,k}}(\mathbf{y},\mathbf{z})$ . We shall prove the following existance properties of Hamiltonian path: (1) for n驴k驴3 or (n,k)=(3,1), there exists a Hamiltonian path R(x,y,z;l) from x to z such that d R(x,y,z;l)(x,y)=l; (2) for n驴k=2 and n驴5, there exists a Hamiltonian path R(x,y,z;l) except for the case that x, y, and z are adjacent to each other.