Desargues Configuration
DesarguesConfiguration
The Desargues configuration is a 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem.
Its Levi graph is the Desargues graph.
PetersenGraphFromDesarguesConfiguration
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).
See also
Configuration, Desargues Graph, Desargues' TheoremExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
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. London 177, 1-70, 1886.Referenced on Wolfram|Alpha
Desargues ConfigurationCite this as:
Weisstein, Eric W. "Desargues Configuration." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DesarguesConfiguration.html