Definition:Spanning Tree

Definition
Let $G$ be a connected graph.

A spanning tree for $G$ is a spanning subgraph of $G$ which is also a tree.

Clearly a tree is its own spanning tree:

As a tree $T$ of order $n$ has $n-1$ edges, its spanning tree must also contain $n-1$ edges, and those must be the same ones as in $T$.

Creation of a Spanning Tree
There are two ways of creating a spanning tree for a given graph $G$: