The Petersen graph was described by Kempe (1886) as the graph whose vertices corresponding to the points of the Desargues configuration
and edges to pairs of points that do not lie on lines that are part of the configuration.
Graphs produced from configurations in this way have been termed ordinary
(line) graphs by Ed Pegg, Jr. (pers. comm., Sep. 11, 2024).
Coxeter, H. S. M. "Self-Dual Configurations and Regular Graphs." Bull. Amer. Math. Soc.56, 413-455, 1950.Gropp,
H. "Configurations and Their Realization." Discr. Math.174,
137-151, 1997.Grünbaum, B. Configurations
of Points and Lines. Providence, RI: Amer. Math. Soc., pp. 1-2, 2009.Kempe,
A. B. "A Memoir on the Theory of Mathematical Form." Philos. Trans.
Royal Soc. London177, 1-70, 1886.
configuration of ten
lines intersecting three at a time in 10 points
which arises in Desargues' theorem.
