Fault-Tolerant Maximal Local-Connectivity on the Bubble-Sort Graphs

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processor and communication links, respectively. The local connectivity of two vertices is defined as the maximum number of internally vertex-disjoint paths between them. In this paper, we define two vertices to be maximally local-connected, if the maximum number of internally vertex-disjoint paths between them equals the minimum degree of these two vertices. Moreover, we introduce the one-to-many version of connectivity. We show that an n-dimensional bubble-sort graph is maximally local-connected, even if there are at most n - 3 faulty vertices in it, and prove that it is also (n - 1)-fault-tolerant one-to-many maximally local-connected.