A spanning tree of a (connected) graph $G$ is a connected, acyclic subgraph of $G$ that contains all of the vertices of $G$ Below is an example of a spanning tree $T$ where the edges in $T$ are drawn as solid lines and the edges in $G$ but not in $T$ are drawn as dotted lines.

$$ \xymatrix{ \bullet \ar@{.}[dddd] \ar@{-}[ddr] \ar@{.}[rrr] &&& \bullet \ar@{.}[ddll] \ar@{-}[dd] \ar@{.}[drr] \\ &&&&&\bullet \ar@{-}[dll] \ar@{.}[d] \\ &\bullet\ar@{-}[ddl]\ar@{-}[dr]\ar@{.}[rr] && \bullet\ar@{-}[dl]\ar@{.}[dr]\ar@{-}[rr] &&\bullet\ar@{-}[dl] \\ &&\bullet\ar@{.}[dll]\ar@{-}[dr]\ar@{.}[rr]&&\bullet\ar@{.}[dl] \\ \bullet\ar@{.}[rrr]&&&\bullet } $$

For any tree there is exactly one spanning tree: the tree itself.