Give an example of a simple, undirected, and unweighted graph G$($V$,$ E$)$ that has a single source shortest path tree which a depth$-$first traversal will not return for any ordering of its vertices. Your answer must $($a$)$ Provide a drawing of the graph G$.($Note: We have provided TikZ code below if you wish to use IATEX to draw the graph. Alternatively, you may hand$-$draw G and embed it as an image below, provided that $($i$)$ your drawing is legible and $($ii$)$ we do not have to rotate our screens to grade your work.$]($b$)$ Specify the single source shortest path tree T $=($V$.$ Er$)$ by specifying Er and also specifying the root s $$ V$.$ Note: You may again hand$-$draw this tree. If you wish, you may clearly mark the edges of T on your drawing of G$.$ Please make it easy on the graders to identify the edges of T$.]($c$)$ Include a clear explanation of why the depth$-$first search algorithm we discussed in class will never produce T for any orderings of the vertices.