From this, I could understand what a functional graph is. But how can we find a function $f$ such that f is an isomorphism between two fuctional graph, $H$ and $G$ given by fuctions $h(x)$ and $g(x)$ respectively.
To avoid deciding upon whether those graphs are isomorphic or not let us assume that both graphs are cycles of length $n$. And as far as I can think about is that two cycles of same length must be isomorphic.