Problem $2-$ Spanning tree $q$

One application of the DFS algorithm is to generate a spanning tree for a graph, that is$,$ an acyclic graph

for the nodes reachable from a given starting node. Write a function

function spanning$\_$tree$($g::Graph, start$)$

which returns a new graph gtree with the same vertices as $g,$ but only the edges that are traversed

by the DFS method starting from vertex start. That is$,$ an edge from ivertex to a neighbor $nb$ is

only included in if the DFS method visits $nb.$

Hint: First initialize gtree to a graph with no edges $($but the same

as $g,$ for plotting$).$

Then you run the DFS method and add edges to gtree.