a) Is it possible to construct a simple graph with degree sequence 2, 2, 2, 2, 2, 3, 3, 3 Either construct an example of such a graph or say why it is not possible to do so. b) Construct two non-isomorphic trees with degree sequence 1, 1,1, 2, 2, 3. Justify your answer.

Two simple graphs are if there is a bijection from the vertices of the first graph to the vertices of the second such that two vertices are adjacent in the first graph if and only if their images are adjacent in the second.

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.