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

Matching preclusion and strong matching preclusion of the bubble-sort star graphs