Edge Fault Tolerance Of Super Edge Connectivity For Several Families Of Interconnection Networks

A system can be defined as an object or a group of elements, which are connectedto form a colony with specific functions or objectives. The function a system can realizeis determined by the function of elements in it and the way that they are connected.The way elements are connected in the system is called the interconnection networkof the system, or networks for short. Logically, the interconnection network allocatesthe connecting mode of elements in a system. An interconnection network can bepresented by a graph. Vertices of the graph stand for elements in the network, and edgesof the graph stand for physical links between elements. When designing a network, oneimportant factor which should be taken into consideration is the fault tolerance. Whenone element or link fails, its obligation is supposed to be fulfilled by other elementsor links in the network. In this paper, fault tolerance of an interconnection network isreferred to the characteristic that the network can keep working with malfunction ofsome elements or links.Let G = (V, E) be a graph with edge connectivityλ. G is maximum edge con-nected ifλ=δ(G), whereδ(G) is the minimum degree of G. Moreover, G is super-λifit is maximum edge connected and every minimum edge cut isolates one of the vertexof G. A super-λgraph G is called m-super-λif for any edge set S - E with |S |≤m,G-S is still super-λ. The maximum integer of such m is called the edge fault toleranceof super edge connectivity of G. In this paper, we discuss the edge fault tolerance ofsuper edge connectivity of several families of interconnection networks.For network G(G₀,G₁; M), we estimate the bound of its edge fault tolerance ofsuper edge connectivity. Furthermore, if G₀ and G₁ are both regular, we can refine thelower bound of the index. Also, we discussed the Sλof hypercube as a particular caseof G(G₀,G₁; M). As for network G(G₀,G₁,···,G_r-1;μ), we estimate the upper andlower bound of its Sλ. For interconnection network G(G₀,G₁; D) and its two particularcase G(G₀,G₁; L) and folded hypercube, we discuss the bound of their Sλ. Finally, we estimate the exact value of network S P_n.