2 problems

Let $p\geq 3$, let $G^{(p)}_{n+1}$ contain the copy $AG^{(p)}_n$, and let $S_{n_0}$ be the recursively defined border set. Let $a$ be the vertex labeled $A^{n_0+1}$, and call a ver…

Let $p\geq 3$, let ${\cal A}_p$ be an alphabet of $p$ letters, and let $A,B\in{\cal A}_p$. For $n\geq 2$, consider vertices labeled $A^n$ and $B^n$. A vertex on a path is special i…