The (strong) matching preclusion of bubble-sort star graphs

Abstract

The (strong) matching preclusion number is a measure of the performance of the interconnection network in the event of (vertex and) edge failure, 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. 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 get 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.