Two graphs G1 (V1, E1) and G2 (V2, E2), such that V1 V2 1, 2, , n are isomorphic if there is a one one, onto function 1, 2, , n 1, 2, , n such that for every i, j 1, 2, , n E1 E2 Show that the following decision problem in in NP Problem Isomorphism Input Instance Two graphs G1 (V1, E1) and G2 (V2, E2) where V1 V2 1, 2, , n Decision Are G1 and G2 isomorphic

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Question: Two graphs G1 = (V1, E1) and G2 = (V2, E2), such that V1 = V2 = {1, 2, , n} are isomorphic if there

Two graphs G1 = (V1, E1) and G2 = (V2, E2), such that V1 = V2 = {1, 2, , n} are isomorphic if there is a one-one, onto function : {1, 2, , n} {1, 2, , n} such that for every i, j {1, 2, , n}

E1 <(i), (j)> E2

Show that the following decision problem in in NP.

Problem: Isomorphism Input

Instance: Two graphs G1 = (V1, E1) and G2 = (V2, E2) where V1 = V2 = {1, 2, , n}

Decision: Are G1 and G2 isomorphic?

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