question 7

Determine all diagraphs of order 4 and size 4. Prove or disprove: For every integer n greaterthanorequalto 2, there exists a digraph D of order n such that for every two distinct vertices u and v of D, od u notequalto od v and id u notequalto id v. Prove or disprove; there exists a nontrivial diagraph D in which no two vertices of D have the same outdegree but every two vertices of D have the same indegree. Prove or disprove: No diagraph contains as odd numbers of vertices odd outdegree or an odd number of vertices of odd numbers of vertices of odd indegree