The square graph is the cycle graph 
. It is isomorphic to the complete
bipartite graph 
.
Despite the similar name, the square graph is unrelated to the graph square, which is the second graph power of a graph.
The square graph is implemented in the Wolfram Language as GraphData["SquareGraph"].
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 distinct pairs having the same first coordinate or the same second coordinate.
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.
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