Edge-fault-tolerant strong Menger edge connectivity of bubble-sort star graphs

Abstract

The connectivity and edge connectivity of interconnection network determine the fault tolerance of the network. An interconnection network is usually viewed as a connected graph, where vertex corresponds processor and edge corresponds link between two distinct processors. Given a connected graph G with vertex set V (G) and edge set E(G), if for any two distinct verticespaths between u and v, then G is strongly Menger edge connected. Let m be an integer with m ≥ 1. If G − F e remains strongly Menger edge connected for any F e ⊆ E(G) with |F e | ≤ m, then G is m-edge-fault-tolerant strongly Menger edge connected. If G − F e is strongly Menger edge connected for any F e ⊆ E(G) with |F e | ≤ m and δ(G−F e ) ≥ 2, then G is m-conditional edge-fault-tolerant strongly Menger edge connected.In this paper, we consider the n-dimensional bubble-sort star graph BS n . We show that BS n is (2n − 5)-edge-fault-tolerant strongly Menger edge connected for n ≥ 3 and (6n − 17)-conditional edge-fault-tolerant strongly Menger edge connected for n ≥ 4. Moreover, we give some examples to show that our results are optimal.