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The connectivity and edge connectivity of interconnection network determinethe fault tolerance of the network. An interconnection network is usuallyviewed as a connected graph, where vertex corresponds processor and edgecorresponds link between two distinct processors. Given a connected graph $G$with vertex set $V(G)$ and edge set $E(G)$, if for any two distinct vertices$u,v\in V(G)$, there exist $\min\{d_G(u),d_G(v)\}$ edge-disjoint paths between$u$ and $v$, then $G$ is strongly Menger edge connected. Let $m$ be an integerwith $m\geq1$. If $G-F_e$ remains strongly Menger edge connected for any$F_e\subseteq E(G)$ with $|F_e|\leq m$, then $G$ is $m$-edge-fault-tolerantstrongly Menger edge connected. If $G-F_e$ is strongly Menger edge connectedfor any $F_e\subseteq E(G)$ with $|F_e|\leq m$ and $\delta(G-F_e)\geq2$, then$G$ is $m$-conditional edge-fault-tolerant strongly Menger edge connected. Inthis paper, we consider the $n$-dimensional bubble-sort star graph $BS_n$. Weshow that $BS_n$ is $(2n-5)$-edge-fault-tolerant strongly Menger edge connectedfor $n\geq3$ and $(6n-17)$-conditional edge-fault-tolerant strongly Menger edgeconnected for $n\geq4$. Moreover, we give some examples to show that ourresults are optimal.

Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star graphs