$1-$ Is there any directed graph$($digraph$)$ with $5$ vertices and $21$ arcs?

$2-$ Check if a graph is strongly connected by Warshall algorithm.

$3-$ Define a matching in a graph. What is maximal matching, maximum matching, perfect

matching. Is every maximum matching is maximal? What about it is converse?

$4-$ Describe the greedy matching algorithm.