Leaf power

In the mathematical area of graph theory, a k-leaf power of a tree ${\displaystyle T}$ is a graph ${\displaystyle G}$ whose vertices are the leaves of ${\displaystyle T}$ and whose edges connect pairs of leaves whose distance in ${\displaystyle T}$ is at most ${\displaystyle k}$. That is, ${\displaystyle G}$ is an induced subgraph of the graph power ${\displaystyle T^{k}}$, induced by the leaves of ${\displaystyle T}$. For a graph ${\displaystyle G}$ constructed in this way, ${\displaystyle T}$ is called a k-leaf root of ${\displaystyle G}$.

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Wikipedia