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Graph Theory

Q5) Give a proof, using mathematical induction, of the following: Theorem: The complete bipartite graph Kn. has n2 edges. Hint: You can use exactly the same scheme seen in class: use the fact that Kn. is a subgraph of Kn+1,n+1 and figure out how many extra edges need to be added to Kn,n to form Kn+ln+1. Then verify that if the hypothesis that Knn has n2 edges is true, then Kn+1n+1 actually has (n +1)2 edges.

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