McKay–Praeger conjecture for fixed-valency vertex-transitive graphs

For fixed $d\geq 3$, let $VT_d(n)$ be the number of isomorphism classes of $d$-valent vertex-transitive graphs of order at most $n$, and let $CAY_d(n)$ count the corresponding Cayley graphs. McKay–Praeger conjecture. For every $d\geq 3$,

$$\frac{CAY_d(n)}{VT_d(n)}\to 1 \qquad (n\to\infty).$$

This asserts that almost all fixed-valency vertex-transitive graphs are Cayley graphs. It is presented as an open conjecture; the source attributes the general almost-all formulation to McKay and Praeger.