The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as GraphData["FolkmanGraph"] and illustrated above in several symmetric embeddings.
The Folkman graph has eight distinct generalized LCF notations, three with exponent 5 and five with exponent 1, illustrated above.
The Folkman graph has graph spectrum