On self-antipodal graphs (Q1109041)

Given a graph G, its antipodal graph A(G) has the same point set V(G) as that of G with two points u, v defined to be adjacent whenever the distance between u and v in G is equal to the diameter of G. A graph G is then called self-antipodal if it is isomorphic to A(G). It is shown here that every self-antipodal graph is either a bi-p.s.c. graph of diameter 3 or is nonbipartite, and that in each case infinitely many such graphs exist.