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Integral Embedding


An integral embedding of a graph is a straight line embedding whose edges have integer lengths. Under this topological definition, the vertices occupy distinct points and the edges meet only at common endpoints. In the plane, this is called a plane integral drawing (Kemnitz and Harborth 2001).

Some geometric literature also uses integral embedding for any integral drawing. In that usage, the integer edge-length condition does not prevent intersections, so the resulting drawing need not be a topological embedding.


See also

Graph Embedding, Integral Drawing, Planar Graph Embedding, Straight Line Embedding, Unit-Distance Embedding

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References

Kemnitz, A. and Harborth, H. "Plane Integral Drawings of Planar Graphs." Disc. Math. 236, 191-195, 2001. https://doi.org/10.1016/S0012-365X(00)00442-8.

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Integral Embedding

Cite this as:

Weisstein, Eric W. "Integral Embedding." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegralEmbedding.html

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