Generalized edge-toughness

Abstract

A communication network may be represented as a graph G=(V,E), where the nodes of the network (hosts, packet switches) and its communication links are modelled by the vertices and the edges of the graph respectively. The vulnerability of a communication network is defined as the measurement of the global strength of its underlying graph. A vulnerability index introduced by D. Gusfield (1983) of a graph G, called edge-toughness, and denoted by /spl eta/(G), tells us that in order to split a graph G into k+/spl omega/(G), where /spl omega/(G) represents the number of connected components of G, we must then remove at least k/spl eta/(G) edges from G, thus /spl eta/(G) measures how tough it is to break up G. In this paper we propose a generalized edge-toughness index of a graph G, /spl eta//sub K/(G). This index tells us how tough it is to break up the communication between the vertices of an arbitrary set K/spl sube/V, |K|/spl ges/2. Moreover we show that some of the properties of edge-toughness for the particular case K=V are extended to any arbitrary subset K/spl sube/V.