Lattice Graph

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space 👁 R^n
that forms a regular tiling. Examples include grid graphs and triangular grid graphs.

Rook graphs are sometimes also known as lattice graphs (e.g., Brouwer). Another class of graph sometimes given this name are the "lattice graphs" of Ball and Coxeter (1987, p. 305) obtained by taking the 👁 n^2
ordered pairs of the first 👁 n
positive integers as vertices and drawing an edge between all pairs having exactly one number in common.

See also

Grid Graph, Rook Graph, Square Graph, Triangular Grid Graph

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References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, 1987.Brouwer, A. E. "Lattice Graphs." http://www.win.tue.nl/~aeb/drg/graphs/Hamming.html.

Referenced on Wolfram|Alpha

Lattice Graph

Cite this as:

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