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.
