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We construct an infinite ternary tree $\mathfrak{L}$ whose root is the knightand whose vertices are all skew free leapers. We define the descent of a skewfree leaper to be its "address" within $\mathfrak{L}$. We introduce threetransformations which relate the leaper graphs of a skew free leaper to theleaper graphs of its three children in $\mathfrak{L}$. By starting with theknight and then applying these transformations so as to advance throughout$\mathfrak{L}$, we can establish theorems about all skew free leapers. We callthis proof technique induction on descent and with its help we resolve a numberof questions about leaper graphs.

Induction on Descent in Leaper Graphs