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The triangular grid graph is the lattice graph obtained by interpreting the order- triangular grid as a graph, with the intersection of grid lines being the vertices and the line segments between vertices being the edges. Equivalently, it is the graph on vertices with being nonnegative integers summing to such that vertices are adjacent if the sum of absolute differences of the coordinates of two vertices is 2 (West 2000, p. 391).

Note that the alternate convention of calling the triangular lattice graph with (instead of ) points along each of the three boundary lines the "-triangular grid graph" is also commonly encountered. For example, the graph called the triangular grid graph by Wagon (2014) is in the notation and indexing of West (2000, pp. 390-391).

The graph bandwidth of is (West 2000, p. 392).

is also the triangular honeycomb king graph of order (Wagon 2014), i.e., the connectivity graph of possible moves of a king chess piece on a hexagonal chessboard. is called -supertriangle in the graph catalog of the American Institute of Mathematics.

See also

Hanoi Graph, Lattice Graph, Sierpiński Gasket Graph, Triangular Grid, Triangular Honeycomb King Graph

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References

American Institute of Mathematics. "Graph Catalog: Families of Graphs." https://aimath.org/WWN/matrixspectrum/catalog2.html.American Institute of Mathematics. "AIM Minimum Rank Graph Catalog." http://admin.aimath.org/resources/graph-invariants/minimumrankoffamilies/#/super.House of Graphs. Triangular Grid Graphs. Singleton Graph, Triangle K3, Triangular Grid Tr2, Triangular Grid Tr3, and Triangular Grid Tr4.Wagon, S. "Graph Theory Problems from Hexagonal and Traditional Chess." College Math. J. 45, 278-287, 2014. https://doi.org/10.4169/college.math.j.45.4.278.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 390-392, 2000.

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Triangular Grid Graph

Cite this as:

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

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