2-Restricted Edge Connectivity of Wheel Networks

Abstract

The g -restricted edge connectivity ( g -REC) is an efficient index in evaluating the reliability and fault tolerance of large-scale processing systems. Assume that G = V , E is a simple connected graph and F ⊆ E . The g -REC of G , denoted by λ g G , is the minimum F such that G − F is disconnected and any component has at least g nodes. The n -dimensional wheel network CW n , a kind of Cayley graph, possesses many desired features. In this paper, we establish that λ 2 CW n is 4 n − 6 for n ≥ 5 , and CW n is λ 2 -optimal.