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Hamiltonian cycles of balanced hypercube with disjoint faulty edges

Published: 18 October 2024 Publication History

Abstract

The balanced hypercube B H n, a variant of the hypercube, is a novel interconnection network topology for massive parallel systems. It is showed in [Theor. Comput. Sci. 947 (2023) 113708] that for any edge subset F of B H n there exists a fault-free Hamiltonian cycle in B H n − F for n ≥ 2 with | F | ≤ 5 n − 7 if the degree of every vertex in B H n − F is at least two and there exist no f 4-cycles in B H n − F. In this paper, we consider the existence of Hamiltonian cycles of B H n when F is a matching (a set of disjoint edges), and show that each edge e ∉ F lies on a fault-free Hamiltonian cycle of B H n − F with n ≥ 2. The number of faulty edges in F can be up to 2 2 n − 1, which is exponential to the dimension n.

Highlights

The balanced hypercube admits a Hamiltonian cycle after the removal of any matching.
The matching can be a perfect matching.
The largest number of faulty edges in the matching is exponential to the dimension.

References

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          Published In

          cover image Information Processing Letters
          Information Processing Letters  Volume 187, Issue C
          Jan 2025
          115 pages

          Publisher

          Elsevier North-Holland, Inc.

          United States

          Publication History

          Published: 18 October 2024

          Author Tags

          1. Interconnection network
          2. Balanced hypercubes
          3. Hamiltonian cycle
          4. Disjoint faulty edges

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