A Latin square graph is the simple graph associated with a Latin square 
of positive integer order
. Its vertices are the
cells of 
, and two distinct cells are adjacent
if they share a row or column or contain the same symbol (Bailey et al. 2019).
It is regular of vertex degree 
. For 
, it strictly contains the
rook
graph as a spanning subgraph. At order 1
both graphs are the singleton
graph, while at order 2 the Latin square graph is the complete
graph 
and the rook graph is the square
graph 
.
