THEOREM OF THE DAY: Cameron’s Theorem on Distance Transitive Graphs

Theorem

For any integer k > 2 there exist only finitely many finite distance-transitive k-regular graphs.

Click on the image.

Norman Biggs and Derek H. Smith proved in 1971 that there are exactly twelve 3-regular distance transitive graphs. It is at first sight very surprising that even a strong condition on symmetry should defeat the variety available in arbitrarily large graphs. Peter Cameron’s deep theorem (1982) shows that this defeat applies even when arbitrarily many adjacencies are allowed.