Abstract
The connectivity plays an important role in measuring the fault tolerance and reliability of interconnection networks. The generalized [Formula: see text]-connectivity of a graph [Formula: see text], denoted by [Formula: see text], is an important indicator of a network’s ability for fault tolerance and reliability. The bubble-sort star graph, denoted by [Formula: see text], is a well known interconnection network. In this paper, we show that [Formula: see text] for [Formula: see text], that is, for any three vertices in [Formula: see text], there exist [Formula: see text] internally disjoint trees connecting them in [Formula: see text] for [Formula: see text], which attains the upper bound of [Formula: see text] given by Li et al. for [Formula: see text].
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