Isolated Rupture in Composite Networks

Abstract

Computer networks are prone to targeted attacks and random failures. Robustness is a measure of an ability of a network to continue functioning when part of the network is either naturally damaged or targeted for attack. The study of network robustness is a critical tool in the characterization and understanding of complex interconnected systems. There are several proposed graph metrics that predicates network resilience against such attacks. Isolated rupture degree is a novel graph-theoretic concept defined as a measure of network vulnerability. Isolated rupture degree is argued as an appropriate measure for modelling the robustness of network topologies in the face of possible node destruction. In this paper, the relationships between isolated rupture degree and some other graph parameters such as connectivity, covering number, minimum vertex degree are established. The isolated rupture degrees of [Formula: see text]-free graphs, middle graphs, corona graphs of a middle graph and a complete graph [Formula: see text] on two vertices are evaluated, then compared and the more stable graph types are reported. A sharp upper bound for the isolated rupture degree of middle graphs is established.