The 
-triangular
honeycomb rook graph 
is a graph consisting of vertices
on a triangular honeycomb board with
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 
-triangular
honeycomb rook graph is therefore isomorphic to the graph
disjoint union complete graphs 
. The 1-triangular honeycomb
rook graph is isomorphic to the singleton graph 
.
Triangular honeycomb rook graphs are block, chordal, claw-free, integral, line, nongeometric, perfect, Ptolemaic, strongly perfect, weakly perfect, and well-covered.
These graphs have no perfect matching.
The 
-triangular
honeycomb rook graph has domination number and
independence number 
(DeMaio and Tran 2013).
Triangular honeycomb rook graphs are implemented in the Wolfram Language as GraphData[
"TriangularHoneycombRook",
n
].
