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arXiv · 2208.08601

Hamiltonian cycles of balanced hypercube with more faulty edges

Ting Lan·Huazhong Lü
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Abstract

The balanced hypercube $BH_{n}$, a variant of the hypercube, is a novel interconnection network for massive parallel systems. It is known that the balanced hypercube remains Hamiltonian after deleting at most $4n-5$ faulty edges if each vertex is incident with at least two edges in the resulting graph for all $n\geq2$. In this paper, we show that there exists a fault-free Hamiltonian cycle in $BH_{n}$ for $n\ge 2$ with $\left | F \right |\le 5n-7$ if the degree of every vertex in $BH_{n}-F$ is at least two and there exists no $f_{4}$-cycles in $BH_{n}-F$, which improves some known results.

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Ting Lan, Huazhong Lü. 2022-08-18. Hamiltonian cycles of balanced hypercube with more faulty edges. https://doi.org/10.1016/j.tcs.2023.113708

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