a survey on complexity of integrity parameter

many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. in this paper we discuss integrity and its properties in vulnerability calculation. the integrity of a graph g, i(g), is defined to be min(| s | +m(g − s)) where s ⊂ v (g) and m(g − s) is the maximum order of the components of g − s. similarly the edge-integrity of g is i′(g) := min(| s | +m(g − s)) where now s ⊆ e(g). here and through the remaining sections, by an i-set (with respect to some prescribed graph g) we will mean a set s ⊂ v (g) for which i(g) =| s | +m(g − s). we define an i′-set similarly. in this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation.