Symmetry
In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the start of the Foster census. Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs-Smith graph. W. T. Tutte classified the symmetric cubic graphs by the smallest integer number s such that each two oriented paths of length s can be mapped to each other by exactly one symmetry of the graph. He showed that s is at most 5, and provided examples of graphs with each possible value of s from 1 to 5.
Semi-symmetric cubic graphs include the Gray graph (the smallest semi-symmetric cubic graph), the Ljubljana graph, and the Tutte 12-cage.
The Frucht graph is one of the two smallest cubic graphs without any symmetries: it possesses only a single graph automorphism, the identity automorphism.
Read more about this topic: Cubic Graph
Famous quotes containing the word symmetry:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)