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Graph Isomorphism

Let V(G) be the vertex set of a simple graph and E(G) its edge set. Then a graph isomorphism from a simple graph G to a simple graph H is a bijection f:V(G)->V(H) such that uv in E(G) iff f(u)f(v) in E(H) (West 2000, p. 7).

If there is a graph isomorphism for G to H, then G is said to be isomorphic to H, written G=H.

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. As a result, the special complexity class graph isomorphism complete is sometimes used to refer to the problem of graph isomorphism testing.

See also

Graph Automorphism, Graph Isomorphism Complete, Isomorphic, Isomorphic Graphs, Isomorphism

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References

Du, D.-Z. and Ko, K.-I. Theory of Computational Complexity. New York; Wiley, p. 117, 2000.Garey, M. R. and Johnson, D. S. Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman, pp. 155-156, 1983.McKay, B. "Practical Graph Isomorphism." Congr. Numer. 30, 45-87, 1981.Skiena, S. "Graph Isomorphism." §5.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 181-187, 1990.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.

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Graph Isomorphism

Cite this as:

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

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