论文标题
平衡超立方体的哈密顿周期和更故障的边缘
Hamiltonian cycles of balanced hypercube with more faulty edges
论文作者
论文摘要
平衡的HyperCube $ bh_ {n} $是HyperCube的变体，是用于大规模并行系统的新型互连网络。众所周知，如果每个顶点在所有$ n \ geq2 $中至少有两个边缘，则删除最多$ 4N-5 $有故障的边缘后，平衡的HyperCube仍然是Hamiltonian。在本文中，我们证明存在$ n \ ge 2 $ with $ \ left | f \ right | \ le 5n-7 $如果$ bh_ {n} -f $中的每个顶点的度量至少为两个，则没有$ f_ {4} $ - $ bh_ {n} -f $中的循环，从而改善了一些已知的结果。
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.
