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Just Rigid


A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) condition that a graph be just rigid is that

 E=2V-3,

where E is the number of edges (bars) and V is the node of vertices (i.e., pivots; Coxeter and Greitzer 1967, p. 56).


See also

Rigid Graph

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References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 56, 1967.Lamb, H. Statics, Including Hydrostatics and the Elements of the Theory of Elasticity, 3rd ed. London: Cambridge University Press, 1928.

Referenced on Wolfram|Alpha

Just Rigid

Cite this as:

Weisstein, Eric W. "Just Rigid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JustRigid.html

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