Problem $1$: $(25$ points$)$Let G$-($V$.$E$)$ be the following graph: V$=(1,2,3,4,5,6,7,8,9,10,11,12\}$ and E$=(1,2,(2,3),(3,4),(4,5),(1,6),(62),(2,7),7,3),2,8),(8,3),(3,9),9,4,4,10),(4,11),(10,11),(4,12),(12,5)$;$.$ Note: In the BFS and DFS below, break ties by always visiting the smallest unvisited neighbor first.a$)$ Perform BFS on G from node $1,$ showing the BFS tree.b$)$ Perform DFS on G from node $1,$ showing the tree and backward edges, compute the L and DFN of every node, identify the articulations points, and indicate the reason why those nodes are articulation points.