Laman's Theorem
Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having n^' graph vertices and e^' graph edges.
See also
Laman Graph, Rigid GraphExplore with Wolfram|Alpha
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References
Laman, G. "On Graphs and Rigidity of Plane Skeletal Structures." J. Engineering Math. 4, 331-340, 1970.Pollaczek-Geiringer, H. "Über die Gliederung ebener Fachwerke." Zeitschr. f. Angewandte Math. u. Mechanik 7, 58-72, 1992.Referenced on Wolfram|Alpha
Laman's TheoremCite this as:
Weisstein, Eric W. "Laman's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LamansTheorem.html