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 
.
