Extraconnectivity of graphs with large girth (Q1322225)

Let \(G\) be a graph and let \(P\) be a graph-theoretic property. The conditional connectivity of \(G\) with respect to \(P\) is the minimum cardinality of a set of vertices (if any) whose deletion disconnects the graph \(G\) and every remaining component has property \(P\). The authors define the new notion of extraconnectivity of graphs, study the relationship to the concept of conditional connectivity, and give some sufficient conditions.