The symmetric (2k, k)-graphs

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 subset of or equal to V(G) wit h \X\ less than or equal to k. Mader conjectured that for k greater than or equal to 3 the graph K2k + 2 - (1-factor) is the unique (2k, k)-graph. We settle this conjecture for strongly regular graphs, for edge transitive gra phs, and for vertex transitive graphs. (C) 2000 John Wiley & Sons, Inc.