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Square Graph


SquareGraph

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2).

Like all cycle graphs, the line graph of C_4 is isomorphic to itself.

SquareGraphConstruction

A generalization of the square graph Sq_n is the "lattice graph" of Ball and Coxeter (1987, p. 305) obtained by taking the n^2 ordered pairs of the first n 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 Sq_3.

SquareGraphs

The square graphs of small orders are illustrated above. Sq_1 is isomorphic to the singleton graph and Sq_2 to the usual square graph.


See also

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

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