Laman's theorem characterizes minimal generic planar rigidity of finite simple graphs by graph edge counts (Laman 1970). Let a
finite simple graph 
with 
have exactly 
graph edges, where 
is the number of graph vertices
in 
. Then 
is "generically" rigid
in 
iff 
for every subgraph
of 
having 
graph vertices and
graph edges.
Laman's Theorem
See also
Laman Graph, Rigid GraphExplore with Wolfram|Alpha
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, 1927. https://doi.org/10.1002/zamm.19270070107.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