Show a Hesse diagram with 5 nodes {1, 2, 3, 4, 5} and 4 edges that has exactly three topological sorting.

You'd like to study social networks. Consider the following 26 people {A,B,C,...,X,Y,Z} in a social network graph. (These people can be thought of as "nodes" or points drawn on a piece of paper.)  Here, we'd like to model "followers." How many different ways can we draw arrows between two people from these 26? Here, "A-->B" (A is a follower of B) is not the same as "B-->A" (B is a follower of A). Order matters here.

What is the minimum number of connected components in the graphs with 18 vertices and 9 edges?

13. How many edges does a tree with 6000 vertices have?

Four students want to take certain classes (1, 2, 3, 4 and 5), shown in the table below: Student Classes a 1, 2, 4 b 2, 3, 5 C d 3, 4 1,5 Create a graph of this situation. Then, use graph coloring to determine the minimum number of colors needed in order to minimize the minimum number of time slots classes can be offered.