On computing the vulnerability of some graphs as average

We investigate the resistance of a communication network to disruption of operation after the failure of certain stations or communication links, we use several vulnerability measures. If we think of a graph as modeling a network, the average lower independence number of a graph is one measure of graph vulnerability. For a vertex v of a graph G = (V, E), the lower independence number iv(G) of G relative to v is the minimum cardinality of a maximal independent set of G that contains v. The average lower independence number of G, denoted by iav(G), is the value |1/V(G)| ?v?V(G) iv(G). In this paper, we define and examine this parameter and consider the average lower independence number of binomial trees and middle graphs of some special graphs. © 2009 Academic Publications.