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Graph isomorphism<br />
Definition<br />
Isomorphism of graphs G 1 (V 1 , E 1 ) and G 2 (V 2 , E 2 ) is a bijection<br />
between the vertex sets ϕ : V 1 → V 2 such that<br />
∀u, v ∈ V 1 (u, v) ∈ E 1 ⇔ (ϕ(u), ϕ(v)) ∈ E 2 .<br />
Facts<br />
• No algorithm, other than brute force, is known for testing<br />
whether two arbitrary graphs are isomorphic.<br />
• It is still an open question (!) whether graph isomorphism is<br />
NP complete.<br />
• Polynomial time isomorphism algorithms for various graph<br />
subclasses such as trees are known.<br />
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