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

The connectivity and edge connectivity of interconnection network determine the fault tolerance of the network. An interconnection network is usually viewed as a connected graph, where vertex corresponds processor and edge corresponds link between two distinct processors. Given a connected graph with vertex set and edge set , if for any two distinct vertices , there exist edge-disjoint paths between and , then is strongly Menger edge connected. Let be an integer with . If remains strongly Menger edge connected for any with , then is -edge-fault-tolerant strongly Menger edge connected. If is strongly Menger edge connected for any with and , then is -conditional edge-fault-tolerant strongly Menger edge connected. In this paper, we consider the -dimensional bubble-sort star graph . We show that is -edge-fault-tolerant strongly Menger edge connected for and -conditional edge-fault-tolerant strongly Menger edge connected for . Moreover, we give some examples to show that our results are optimal.