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# Square Graph

"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.

Cycle Graph, Graph Power, Lattice Graph, Line Graph, Triangle Graph, Triangular Graph

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## References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, 1987.Brualdi, R. and Ryser, H. J. Combinatorial Matrix Theory. New York: Cambridge University Press, p. 153, 1991.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 144, 1990.

## Cite this as:

Weisstein, Eric W. "Square Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SquareGraph.html