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.)
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