Is it possible to have a geodesic whose length is diam (G) for a graph G or is this a contradiction? A u-v geodesic is a u-v path of length d(u,v), but diam(G) is the greatest distance between any vertices of a connected graph G....So is it possible for me to have a geodesic with length diam(G)?
More specifically the problem gives me a picture of a graph and asks me to find an example of a geodesic with length diam (G) or explain why none exist. The graph is like
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Those are the 9 vertices and the lines are edges. Also, there is an edge between r and v and between t and v.