Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On embedding rings into a star-related network
Information Sciences: an International Journal
Honeycomb Networks: Topological Properties and Communication Algorithms
IEEE Transactions on Parallel and Distributed Systems
Honeycomb tori are Hamiltonian
Information Processing Letters
A Unified Formulation of Honeycomb and Diamond Networks
IEEE Transactions on Parallel and Distributed Systems
Ring embedding in faulty honeycomb rectangular torus
Information Processing Letters
Parallel Computing
On embedding cycles into faulty twisted cubes
Information Sciences: an International Journal
Vertex-bipancyclicity of the generalized honeycomb tori
Computers & Mathematics with Applications
The 3*-connected property of pyramid networks
Computers & Mathematics with Applications
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The honeycomb rectangular torus is an attractive alternative to existing networks such as mesh-connected networks in parallel and distributed applications because of its low network cost and well-structured connectivity. Assume that m and n are positive even integers with n=4. It is known that every honeycomb rectangular torus HReT(m,n) is a 3-regular bipartite graph. We prove that in any HReT(m,n), there exist three internally-disjoint spanning paths joining x and y whenever x and y belong to different partite sets. Moreover, for any pair of vertices x and y in the same partite set, there exists a vertex z in the partite set not containing x and y, such that there exist three internally-disjoint spanning paths of G-{z} joining x and y. Furthermore, for any three vertices x, y, and z of the same partite set there exist three internally-disjoint spanning paths of G-{z} joining x and y if and only if n=6 or m=2.