Question

# Given the following definitions:

- 1) A subgraph
*G'*of a graph*G*consists of a

subset of vertices and edges of *G*. A subgraph *G' *is complete if there is an edge between any pair of vertices of *G'*.

*G*is defined as a set

*S*of vertices of

*G*such that there is no edge between any two vertices of

*S*.

Show that finding a complete subgraph of *G* with *k* vertices is NP-complete by reducing from the *q*-Indepedent Set problem (i.e., finding an independent set with *q* vertices).

Note: you should first present the problem in its decision version and then prove the NP-completeness.

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