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Maximally Laman Graph

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A maximally Laman graph is a Laman graph having the maximum possible Laman number among all Laman graphs with the same number of vertices.

MaximalLamanGraphs

The maximal Laman numbers for Laman graphs on n=1, 2, ... vertices are 1, 1, 2, 4, 8, 24, 56, 136, 344, 880, 2288, 6180, 15536, 42780, ... (OEIS A306420; Grasegger 2025). Known maximally Laman graphs are illustrated above.

The kth maximally Laman graph on n vertices will be implemented in a future version of the Wolfram Language as GraphData[{"MaximallyLaman", {n, k}}].

See also

Laman Graph, Laman Number

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References

Grasegger, G. "Explorations on the Number of Realizations of Minimally Rigid Graphs." 7 Feb 2025. https://arxiv.org/abs/2502.04736.Sloane, N. J. A. Sequence A306420 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Maximally Laman Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MaximallyLamanGraph.html

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