For topological space $X$ (connected, path connected etc.), there is classification of coverings of $X$ : for fixed $x_0\in X$, consider $\pi_1(X,x_0)$. Then there is a $1-1$ correspondance between conjugacy class of subgroups of $\pi_1(X,x_0)$ and covering spaces of $X$ (upto isomorphism). We define universal cover of $X$ to be a cover $\tilde{X}$ which is a cover of every cover $Y$ of $X$. This exist and unique up to isomorphism.

Now consider a *graph of groups* $(X,A)$, where $X$ is a graph and $A=(A_v,A_e)$ is a family of groups attached to vertices $v\in V(X)$ and edges $e\in E(X)$ of $X$ with injections from edge groups to end-vertex groups.

In the book *"Trees"-Serre*, the universal cover of $(X,A)$ is defined to be a connected graph $\tilde{X}$ with:

1) a morphism $p\colon \tilde{X}\rightarrow X$ of graphs;

2) an action of $\pi_1(X,x_0)$, $(x_0\in V(X))$ on $\tilde{X}$ such that stabilizer of $\tilde{v}\in p^{-1}(v)$ is isomorphic to vertex group $A_v$, $v\in V(X)$

(In other words, it is a graph, with action of $\pi_1(X,x_0)$, $(x_0\in V(X)$, such the quotient graph of groups $X/\pi_1(X,x_0)$ is isomorphic to given graph of groups).

* Question*: Is there a construction of universal cover of a graph of groups analogous to the construction of universal cover of topological spaces ( i.e. a cover of every cover of given graph of groups).

As an illustration, how can we obtain all coverings of $(X,A)$ where $X$ is the graph $\circ --\circ$ with vertex groups $\mathbb{Z}/l$, and $\mathbb{Z}/n$ and edge group trivial.