do part $1$ and part $2$ fully. Also draw graphs $2.$Given the posted DIRECTED GRAPH:a$)$ Execute a Depth$-$First Search on the graph, with the following conditions:Start from vertex B$.$Follow the "normal DFS$"$ algorithm using DIRECTED edges!NOTE:There are three types of edges on a DFS di$-$graph:Forward edges are edges u v with v not previously visited. Use a solid line Back edges are edges. u v with v already visited. Use a dotted line.Cross edges are edges u $+$ v $($where there is no edge u v$).$ Use a dotted line.b$)$ Are there any directed cycles in the given graph? Identify them by the vertices in order.c$)$ Is this graph strongly connected? $($Is there a directed path between every pair of vertices?$)$