On the extraconnectivity of graphs

Given a simple connected graph G, let K(n) [2(n)] be the minimum cardinality of a set of vertices [edges], if any, whose deletion disconnects G and every remaining component has more than n vertices. For instance, the usual connectivity and the superconnectivity of G correspond to x(0) and ~c(1 ), respectively. This paper gives sufficient conditions, relating the diameter of G with its girth, to assure optimum values of these conditional connectivities.