TOPICS
Search

Triangular Honeycomb Queen Graph

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
TriangularHoneycombQueenGraph

The n-triangular honeycomb queen graph Q_n (DeMaio and Tran 2013) 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, +60 degrees, or -60 degrees line of the chessboard. Note that the n-triangular honeycomb queen graph was termed a hex rook by Gliński (1973) and Wagon (2014) and denoted HR_n by Wagon (2014). The graphs for n=3 and 4 are illustrated above.

Special cases are summarized in the following table.

nisomorphic graph
1singleton graph K_1
2triangle graph C_3
3octahedral graph K_(2,2,2)

Triangular honeycomb queen graphs are bridgeless, connected, Eulerian, Hamilton-connected, Hamiltonian, H-star connected, integral, LCF, regular, rigid, and traceable.

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

See also

Queen Graph, Triangular Grid Graph, Triangular Honeycomb Board

Explore with Wolfram|Alpha

References

DeMaio, H. and Tran, L. "Domination and Independence on a Triangular Honeycomb Chessboard." College Math. J. 44, 307-314, 2013.Gliński, W. Rules of Hexagonal Chess With Examples of First Openings. London: Hexagonal Chess Publications, 1973.Wagon, S. "Graph Theory Problems from Hexagonal and Traditional Chess." College Math. J. 45, 278-287, 2014.

Cite this as:

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

Subject classifications