Suppose we have an $n$-vertex connected graph, $G$. For any given $i, j \in V(G)$, what is the maximum possible number of $k$-length geodesics that can exist between $i$ and $j$, where $1 \lt k \leq n-1$?
What is the maximum possible number of k-length geodesics in an n-vertex connected graph?
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combinatorics
graph-theory