For the following graph, _{1}:

a. Find |(_{1})| and |(_{1})|.

b. Write the relation depicted by _{1} as a set of ordered pairs.

c. Define the adjacency matrix of _{1}.

d. What is the out degree of each node of _{1}? What is the in degree of

each node of _{1}?

e. Could _{1} be a bipartite graph? If no, why? If yes, what is the partition

into two subsets of nodes that makes this a bipartite graph?

f. Is the relation depicted here reflexive? I reflexive? Symmetric? ant symmetric? Asymmetric? transitive? Intransitive?

g. What arcs (if any) would you have to add to this relation to make it transitive