In the
mathematical field of
graph theory, the
Clebsch graph is either of two
complementary graphs on 16 vertices, a 5-
regular graph with 40 edges and a 10-regular graph with 80 edges. The 80-edge variant is the order-5
halved cube graph; it was called the Clebsch graph name by Seidel (1968) because of its relation to the configuration of 16 lines on the quartic surface discovered in 1868 by the German mathematician
Alfred Clebsch. The 40-edge variant is the order-5
folded cube graph; it is also known as the
Greenwood–Gleason graph after the work of , who used it to evaluate the
Ramsey number R(3,3,3) = 17.