In each case below, either draw a tree or graph with the required properties
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In each case below, either draw a tree or graph with the required properties

Question 1

In each case below, either draw a tree or graph with the required properties or prove that it does not exist. In degree sequence, order does NOT matter.

(a) A tree on 8 vertices with degrees 1,1,1,1,1,2,3,4.

(b) A tree on 6 vertices with degrees 1,2,3,2,2,2.

(c) A connected graph on 5 vertices with degrees 2,3,3,5,5.

(d) A connected graph on 6 vertices with degrees 2,2,3,4,4,4.

A graph can have multiple edges or loops.

(Explanation marks are for correct draw or correct explanation. If you can draw, you do not need to explain. See Section 7.6 in Week 7 handout for examples and theory.)

Hint
Mathematicsdegree sequence: A degree sequence when given an undirected graph, is a monotonic nonincreasing sequence of the vertex degrees or the valencies of its graph vertices. Also, the number of degree sequences for a graph of the given order is closely related to the graphical partitions....

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