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Let G be an undirected graph and Gr be its r-th power. We study different issues dealing with the number of edges in G and Gr. In particular, we answer the following question: given an integer r≥2 and all connected graphs G of order n such that Gr≠Kn, what is the minimum number of edges that are added when going from G to Gr, and which are the graphs achieving this bound?
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