Triangular Grid Graph


The triangular grid graph T_n is the lattice graph obtained by interpreting the order-(n+1) 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 (i,j,k) with i,j,k being nonnegative integers summing to n such that vertices are adjacent if the sum of absolute differences of the coordinates of two vertices is 2 (West 2000, p. 391).

The graph bandwidth of T_n is n+1 (West 2000, p. 392).

T_n is also the hexagonal king graph of order n, i.e., the connectivity graph of possible moves of a king chess piece on a hexagonal chessboard.

See also

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

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West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 390-392, 2000.

Cite this as:

Weisstein, Eric W. "Triangular Grid Graph." From MathWorld--A Wolfram Web Resource.