A328060
Number of bipartite Laman graphs on n vertices.
Original entry on oeis.org
1, 1, 0, 0, 0, 1, 1, 5, 19, 123, 871, 8304, 92539, 1210044, 17860267, 293210063, 5277557739, 103177250918, 2174556695546
Offset: 1
- L. Henneberg, Die graphische Statik der starren Systeme, Leipzig, 1911.
- F. Hüffner, tinygraph, software for generating integer sequences based on graph properties.
- Christoph Koutschan, Mathematica program for generating a list of non-isomorphic Laman graphs on n vertices.
- G. Laman, On Graphs and Rigidity of Planar Skeletal Structures, J. Engineering Mathematics, Vol. 4, No. 4, 1970, pp. 331-340.
- Martin Larsson, C program
- A. Nixon and E. Ross, One brick at a time: a survey of inductive constructions in rigidity theory, arXiv:1203.6623 [math.MG], 2012-2013.
- Wikipedia, Laman graph
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Table[Length[
Select[LamanGraphs[n],
BipartiteGraphQ[AdjacencyGraph[G2Mat[#]]] &]], {n, 6, 9}] (* using the program by Christoph Koutschan for generating Laman graphs, see A227117 *)
a(13)-a(15) added using tinygraph by
Falk Hüffner, Oct 20 2019
A371901
Number of unlabeled Laman graphs on n vertices of degree at most 4.
Original entry on oeis.org
1, 1, 1, 1, 3, 10, 37, 189, 1145, 8089, 64683, 571949, 5499343, 56899844, 628729114, 7380050235
Offset: 1
A233288
Number of (3/2,2)-tight graphs with 2n vertices, or kinematic chains with 2n links.
Original entry on oeis.org
1, 1, 2, 16, 230, 6856, 318162, 19819281, 1535380884
Offset: 1
For n=1 the single example (a graph with two vertices and one edge) is represented by familiar mechanical systems including door hinges and pairs of scissors. For n=3 the a(3)=2 solutions are the 6-vertex 7-edge graphs Theta(1,3,3) and Theta(2,2,3), each of which has two degree-three vertices connected by three paths of the given lengths. These correspond respectively to the Watt linkage (two four-bar linkages sharing a pair of adjacent links) and the Stephenson linkage.
- Eric A. Butcher and Chris Hartman, Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar single degree-of-freedom chains, Mechanism and Machine Theory 30 (2005), 1030-1050.
- Martin Larsson, Nauty Laman plugin
- Audrey Lee and Ileana Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (2008), 1425-1437.
- E. E. Peisakh, Structural analysis of planar jointed mechanisms: Current state and problems, J. Machinery Manufacture and Reliability 37 (2008), 207-212.
- Rajesh P. Sunkari and Linda C. Schmidt, Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm, Mechanism and Machine Theory 41 (2006), 1021-1030. This paper sources the 19819281 value for n=8 but contains a typo for n=7.
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