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?$)$