You are a discrete structure engineer in a well know organization, your boss has requested you to find/figure-out all non-isomorphic trees with four vertices.

Kindly handwritten and correctly

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.

A tree has 7 vertices.   (i)  How many edges this tree can have?    (ii) If the degrees of first six vertices are  1,1,1,2,2 and 3 then what is the degree of         next vertex? Show all your work.    (iii) If the degrees of vertices are 1,1,2,2,3,3 and 4 then is it possible to have such           tree? Explain with detail.