Spanning Tree via Depth-First

By simply traversing the graph in depth-first order and keeping track of which edges you traverse as a set S then the graph with vertex set V and edge set S is a spanning tree for the original graph.
Let's perform a couple of examples on this graph:

By simply traversing the graph in depth-first order and keeping track of which edges you traverse as a set S then the graph with vertex set V and edge set S is a spanning tree for the original graph.