The symmetric (2k, k)-graphs
Matthias Kriesell · Journal of Graph Theory · 2001
A noncomplete graph G is called an (n, k)-graph if it is n-connected and G − X is not (n − |X| + 1)-connected for any X ⊆ V(G) with |X| ≤ k. Mader conjectured that for k ≥ 3 the graph K2k + 2 − (1-factor) is the unique (2k, k)-graph. We settle this conjecture for strongly regular graphs, for edge transitive graphs, and for vertex transitive graphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 36: 35–51, 2001