On the rigidity of molecular graphs
نویسندگان
چکیده
منابع مشابه
On the rigidity of molecular graphs
The rigidity of squares of graphs in three-space has important applications to the study of flexibility in molecules. The Molecular Conjecture, posed in 1984 by T-S. Tay and W. Whiteley, states that the square G of a graph G of minimum degree at least two is rigid if and only if G has six spanning trees which cover each edge of G at most five times. We give a lower bound on the degrees of freed...
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Notes on the Rigidity of Graphs
The first reference to the rigidity of frameworks in the mathematical literature occurs in a problem posed by Euler in 1776, see [8]. Consider a polyhedron P in 3-space. We view P as a ‘ panel-and-hinge framework’ in which the faces are 2-dimensional panels and the edges are 1-dimensional hinges. The panels are free to move continuously in 3-space, subject to the constraints that the shapes of ...
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A graph with a trivial automorphism group is said to be rigid. Wright proved [11] that for logn n + ω( 1 n) ≤ p ≤ 1 2 a random graph G ∈ G(n, p) is rigid whp. It is not hard to see that this lower bound is sharp and for p < (1− ) logn n with positive probability aut(G) is nontrivial. We show that in the sparser case ω( 1 n) ≤ p ≤ logn n + ω( 1 n), it holds whp that G’s 2-core is rigid. We concl...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2008
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-008-2287-z