Neighbour-connectivity in regular graphs (Q1074600)

The author gives another generalization of point-connectivity in removing closed neighbourhoods of vertices instead of only vertices. He calls a graph k-neighbour connected, if for any choice of k vertices and then removing these vertices and their neighbours the survival-subgraph is connected and not a clique (a complete subgraph). Then he gives a complete characterization of the class of graphs which are k-regular, contain a k-clique, are k-neighbour connected and are of order \(k^ 2+k\).