Lesson plan
Clebsch graph
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 graph is the dimension-5 halved cube graph; it was called the Clebsch graph 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 version is the dimension-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.
Article summary
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 graph is the dimension-5 halved cube graph; it was called the Clebsch graph 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 version is the dimension-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.
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