  Since a plurality of processors in a distributed computer system working in
parallel, to ensure the fault tolerance and stability of the network is an
important issue in distributed systems. As the topology of the distributed
network can be modeled as a graph, the (strong) matching preclusion in graph
theory can be used as a robustness measure for missing edges in parallel and
distributed networks, which is defined as the minimum number of (vertices and)
edges whose deletion results in the remaining network that has neither a
perfect matching nor an almost-perfect matching. The bubble-sort star graph is
one of the validly discussed interconnection networks related to the
distributed systems. In this paper, we show that the strong matching preclusion
number of an $n$-dimensional bubble-sort star graph $BS_n$ is $2$ for $n\geq3$
and each optimal strong matching preclusion set of $BS_n$ is a set of two
vertices from the same bipartition set. Moreover, we show that the matching
preclusion number of $BS_n$ is $2n-3$ for $n\geq3$ and that every optimal
matching preclusion set of $BS_n$ is trivial.
