Part C Based on the graph provided, answer the following questions by using the DFS algorithm. $[25$ pts $]$

$($CI$).$ Using the DFS algorithm and starting from the smallest index vertex, visit all the rest vertices in the graph above

and print each vertex in the DFS order. Note: when visiting the adjacency nodes of the focused node, ALWAYS choose

the adjacency node with the smallest index first when you do the DFS$.[10$ pts $]$

$($C$2).$ Find back$-$edges for the graphs starting from the smallest index node using the DFS algorithm. $[5$ pts $]$

$($C$3).$ Generate the DFS$-$tree with a clear notation of paths and back$-$edges. Then, based on it$,$ find articulation vertices

for the graphs above from the smallest index node using the DFS algorithm. $[10$ pts $]$