Let G be a connected graph. For all vertices u and v in G, we define the distance d(u,v) to be the least number d such that there is a path between u and v of length d. Prove that for all vertices u, v and w, d(u, w) ? d(u, v) + d(v, w).
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Let P be a shortest path between u and w, and let d(u,w) be the length of this path. Show more…
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