# What is a non constructible graph?

I'm working through "Groups, Graphs and Trees" by John Meier.

In Chapter 5, he states that in a Cayley Graph, $$\Gamma$$ (or indeed any graph), the ball of radius n centred at the vertex v, $$\mathcal{B}(v,n)$$, is the subgraph formed as the union of all paths in $$\Gamma$$ of length $$\le n$$ that start at the vertex $$v$$.

It is then stated that a Cayley graph Γ is constructible if given $$n \in N$$ one can construct $$\mathcal{B}(e,n)$$ in a finite amount of time.

My question is what is an example of a non-constructible graph?

In particular, it is implied that there are finitely generated groups which have non-constructible Cayley graphs. I cannot comprehend what such a group looks like.