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A connected graph $G$ is called strongly Menger edge connected if $G$ hasmin\{deg$_G(x)$, deg$_G(y)$\} edge-disjoint paths between any two distinctvertices $x$ and $y$ in $G$. In this paper, we consider two types of stronglyMenger edge connectivity of the line graphs of $n$-dimensional hypercube-likenetworks with faulty edges, namely the $m$-edge-fault-tolerant and$m$-conditional edge-fault-tolerant strongly Menger edge connectivity. We showthat 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 bestpossible.

Menger-type connectivity of line graphs of faulty hypercubes