How to go from Tree to Total orders

Given a tree $T=(X,E)$, is it guaranteed for any orientation of the edges $E$, there exist a strict total order preserves it?

For instance, let $X=\{x_1,x_2,..x_n\}$ and $E=(x_i,x_{i+1})$ the result is a tree $T$. Let $G$ be directed graph of $T$ (add directions into the set of edges in $T$). is it always the case where there is a total order $\succ$ extend/equals $G$?

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Forgive my ignorance here, by every order you mean every possible directed graph (DAG) of the orientation of the edges? Also, Can I say that every possible orientation of $T$ will result in a DAG and every DAG has a topological ordering (total ordering)? – seteropere Jan 14 '14 at 16:40