Induced subgraph isomorphism problem

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In complexity theory, Induced-Subgraph-Isomorphism is a decision problem. A formal description of the decision problem is as follows.

Induced-Subgraph-Isomorphism(G1, G2)
Input: Two graphs G1=(V1, E1) and a graph G2=(V2, E2) of lesser or equal order to G1.
Question: Is there an injective function f which maps the vertices of G2 to vertices of G1 such that for all vertices x, y in V2, edge (x, y) is in E2 iff and only if the edge (f(x), f(y)) is in E1

This is different from the subgraph isomorphism problem in that the inducted subgraph in G1 cannot have edges which aren't also in G2. In subgraph isomorphism, these "extra" edges may be present.

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