Let G be a graph and let v; w 2 V .G/. The distance from v to w is the length of a This
Chapter 49, Problem 49.13(choose chapter or problem)
Let G be a graph and let v; w 2 V .G/. The distance from v to w is the length of a This exercise develops the notion of distance in graphs. We need this concept later (in Section 52). x y shortest .v; w/-path and is denoted d.v; w/. In case there is no v; w-path, we may either say that d.v; w/ is undefined or infinite. For the graph in the figure, there are several .x; y/-paths; the shortest among them have length 2. Thus d.x; y/ D 2.Prove that graph distance satisfies the triangle inequality. That is, if x; y; z arevertices of a connected graph G, thend.x; z/ d.x; y/ C d.y; z/:
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