Edge fault tolerance of interconnection networks with respect to maximally edge-connectivity

Abstract

The interconnection networks are generally modeled by a connected graph G, and the connectivity of G is an important parameter for reliability and fault tolerance of the network. A connected graph G=(V,E) is maximally edge-connected (or maximally-λ for short) if its edge-connectivity attains its minimum degree. We define a maximally-λ graph G to be m-maximally-λ if G−S is still maximally-λ for any edge subset S⊆E(G) with |S|≤m. The maximum integer of such m, denoted by mλ(G), is said to be the edge fault tolerance of G with respect to the maximally-λ property. In this paper, we discuss the edge fault tolerance for maximally-λ property of two families of interconnection networks, from which we determine the exact values of mλ(G) for some well-known networks.