The symmetric (2k, k)-graphs

A noncomplete graph G is called an (n, k )-graph if it is nconnected and GÿX is not (nÿ | X |‡ 1)-connected for any X V(G ) with | X | k. Mader conjectured that for k 3 the graph K2k‡ 2ÿ (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. ß 2000 John… (More)