论文标题
故障高管线图的Menger型连接性
Menger-type connectivity of line graphs of faulty hypercubes
论文作者
论文摘要
如果$ g $有min \ {deg $ _g（x）$，deg $ _g（y）$ \} $ \} $ \} $ g $ g $，则称为强烈的menger边缘连接。在本文中，我们考虑了两种类型的$ n $二维超同管网络的线图强烈的巨型边缘连接性，其边缘有故障，即$ m $ - edge-edge-degpault-doault-parterant和$ m $ $ $ $ $ $ $ - 条件的边缘耐受耐受耐受性强烈的Menger Edge连接。我们表明，任何$ n $二维超立方体的网络的线路图是$（2N-4）$ - 易于耐受的耐受耐受性的强烈的Menger Edge，以$ n \ geq 3 $ 3 $和$（4n-10）$ - 有条件的边缘耐受耐受性的耐受性强的Menger Edge连接了$ n \ geq 4 $。最大数量有故障的两个界限是最好的。
A connected graph $G$ is called strongly Menger edge connected if $G$ has min\{deg$_G(x)$, deg$_G(y)$\} edge-disjoint paths between any two distinct vertices $x$ and $y$ in $G$. In this paper, we consider two types of strongly Menger edge connectivity of the line graphs of $n$-dimensional hypercube-like networks with faulty edges, namely the $m$-edge-fault-tolerant and $m$-conditional edge-fault-tolerant strongly Menger edge connectivity. We show that the line graph of any $n$-dimensional hypercube-like network is $(2n-4)$-edge-fault-tolerant strongly Menger edge connected for $n\geq 3$ and $(4n-10)$-conditional edge-fault-tolerant strongly Menger edge connected for $n\geq 4$. The two bounds for the maximum number of faulty edges are best possible.
