Edge-disjoint trees passing through prescribed vertices in bubble-sort star graphs

Abstract

The study of edge-disjoint trees is applied in computer communication and parallel routing design when design the large-scale networks. The n-dimensional bubble-sort star graph BSn is a widely studied interconnection network. In this paper, we prove that for any given four vertices of BSn, there are 2n−4 edge-disjoint trees passing through them in BSn for n≥3. Since the generalized k-connectivity κk(G) of a graph G is defined based on edge-disjoint trees passing through k prescribed vertices, we also obtain that κ4(BSn)=2n−4, where n≥3. Note that κ4(BSn)≤δ(BSn)−1=2n−4, this result is optimal.