Measures of vulnerability-the integrity family

In this paper a schema of graphical parameters is proposed. Based on the parameter integrity introduced by Barefoot, Entringer and Swart, members Ψ(G) of this schema have the general form Ψ(G) = min{ |S| + ψ(G − S) : S ⊂ V (G) }, where ψ(G) is another given graphical parameter. Examples include integrity, mean integrity, connectivity and vertex cover number. General results and bounds for the schema are derived. Also, properties which characterize such parameters are considered. The research for this paper was performed while the author was a graduate student at the University of Natal and the Massachusetts Institute of Technology