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 A273468 Number of minimally rigid graphs with n vertices constructible by Henneberg type I moves. 6
 1, 1, 1, 1, 3, 11, 61, 499, 5500, 75635, 1237670, 23352425, 498028767, 11836515526, 310152665647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A graph is called rigid if, when we fix the length of each edge, it has only finitely many embeddings in the plane. A graph is called minimally rigid (or a Laman graph) if there is no edge that can be omitted while keeping the rigidity property. Laman graphs can be constructed by applying successively Henneberg moves (of type I or type II), starting with the graph that consists of two vertices joined by an edge. Here we consider Laman graphs that can be obtained by using only Henneberg type I moves, which means: adding one vertex and joining it with two different existing vertices. LINKS Table of n, a(n) for n=1..15. L. Henneberg, Die graphische Statik der starren Systeme, Leipzig, 1911. Christoph Koutschan, Mathematica program G. Laman, On Graphs and Rigidity of Plane Skeletal Structures, Journal of Engineering Mathematics 4 (1970), 331-340. Martin Larsson, C program Wikipedia, Laman graph EXAMPLE A single vertex is rigid. The graph consisting of two vertices joined by an edge is rigid. A triangle is rigid and it is obtained by a single Henneberg type I move. One more such move yields the only Laman graph with four vertices. Also all three Laman graphs with five vertices can be constructed with type I moves. Therefore the first five entries of this sequence agree with A227117. An example of a Laman graph that cannot be constructed using only Henneberg type I moves is the complete bipartite graph K(3,3). MATHEMATICA Table[Length[H1LamanGraphs[n]], {n, 3, 7}] (* see link *) CROSSREFS Cf. A227117. Sequence in context: A185385 A024528 A368880 * A004108 A203007 A343774 Adjacent sequences: A273465 A273466 A273467 * A273469 A273470 A273471 KEYWORD nonn,more AUTHOR Christoph Koutschan, May 23 2016 EXTENSIONS a(13) added by Jose Capco, Dec 07 2018 a(14)-a(15) added by Martin Larsson, Dec 21 2020 STATUS approved

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Last modified September 16 17:53 EDT 2024. Contains 375976 sequences. (Running on oeis4.)