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.