"The" square graphs is the cycle graph 
. It is isomorphic to the complete
bipartite graph 
.
Like all cycle graphs, the line graph of 
is isomorphic to itself.
A generalization of the square graph 
is the "lattice graph" of Ball and Coxeter (1987,
p. 305) obtained by taking the 
ordered pairs of the first 
positive integers as vertices and drawing an edge between
all pairs having exactly one number in common. An example of the construction process
is shown above for 
.
The square graphs of small orders are illustrated above. 
is isomorphic to the singleton
graph and 
to the usual square graph.
