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Graph isomorphism Definition Isomorphism of graphs G 1 (V 1 , E 1 ) and G 2 (V 2 , E 2 ) is a bijection between the vertex sets ϕ : V 1 → V 2 such that ∀u, v ∈ V 1 (u, v) ∈ E 1 ⇔ (ϕ(u), ϕ(v)) ∈ E 2 . Facts • No algorithm, other than brute force, is known for testing whether two arbitrary graphs are isomorphic. 3 / 22
Graph isomorphism Definition Isomorphism of graphs G 1 (V 1 , E 1 ) and G 2 (V 2 , E 2 ) is a bijection between the vertex sets ϕ : V 1 → V 2 such that ∀u, v ∈ V 1 (u, v) ∈ E 1 ⇔ (ϕ(u), ϕ(v)) ∈ E 2 . Facts • No algorithm, other than brute force, is known for testing whether two arbitrary graphs are isomorphic. • It is still an open question (!) whether graph isomorphism is NP complete. 3 / 22
Page 1 and 2: Tree isomorphism Alexander Smal St.
Page 3: Graph isomorphism Definition Isomor
Page 7 and 8: Rooted trees Definition Rooted tree
Page 13 and 14: Rooted trees (part 2) Lemma If ther
Page 19 and 20: Diameter and center Definition The
Page 21 and 22: Diameter and center Definition The
Page 23 and 24: The idea Let’s try to find comple
Page 29 and 30: Candidate 1 Observation The level n
Page 31 and 32: Candidate 1 Observation The level n
Page 33 and 34: Candidate 2 What’s wrong with can
Page 35 and 36: Candidate 2 (part 2) Observation Si
Page 37 and 38: Candidate 3 Conjecture Two trees ar
Page 39 and 40: Candidate 3 Conjecture Two trees ar
Page 41 and 42: Algorithm by Aho, Hopcroft and Ullm
Page 43 and 44: Algorithm by Aho, Hopcroft and Ullm
Page 45 and 46: Understanding AHU algorithm Knuth t
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Understanding AHU algorithm Knuth t
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Understanding AHU algorithm (part 3
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AHU algorithm improvement Observati
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AHU algorithm example Example A a B
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AHU algorithm example Example A 1 2
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AHU algorithm example Example A 1 a
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Resume Resume • We have three uns
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