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Triangular Honeycomb Rook Graph

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TriangularHoneycombRookGraph

The n-triangular honeycomb rook graph R_n is a graph consisting of vertices on a triangular honeycomb board with n vertices along each side, where vertices are connected by an edge if they lie along a horizontal line of the chessboard (DeMaio and Tran 2013).

The n-triangular honeycomb rook graph is therefore isomorphic to the graph disjoint union complete graphs K_1 union K_2 union ... union K_n. The 1-triangular honeycomb rook graph is isomorphic to the singleton graph K_1.

Triangular honeycomb rook graphs and block, chordal, claw-free, integral, line, nongeometric, no perfect matching, perfect, Ptolemaic, strongly perfect, weakly perfect, and well-covered.

The n-triangular honeycomb rook has domination number and independence number n (DeMaio and Tran 2013).

Triangular honeycomb rook graphs are implemented in the Wolfram Language as GraphData[{"TriangularHoneycombRook", n}].

See also

Rook Graph, Triangular Grid Graph, Triangular Honeycomb Board

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References

DeMaio, H. and Tran, L. "Domination and Independence on a Triangular Honeycomb Chessboard." College Math. J. 44, 307-314, 2013.

Cite this as:

Weisstein, Eric W. "Triangular Honeycomb Rook Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriangularHoneycombRookGraph.html

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