ALMOST EVERY GRAPH HAS A FIXED EDGE

An edge e of a graph G is called a fixed edge ii G - e + e' congruent to G implies e' = e, and an isomorphic fixed edge if G - e + e' congru ent to G implies that there exists an automorphism of G - e, which map s the ends of e to the ends of e'. I: is proved that almost every grap h is with all its edges as fixed edges and isomorphic fixed edges, and it is conjectured that all graphs contain isomorphic fixed edges.