Question: 4. (a) Consider the three sequences: a = (1,2, 2, 2, 2, 3, 4, 5, 5, 6), b = (0, 0, 2, 3, 3, 4,

4. (a) Consider the three sequences: a = (1,2, 2, 2, 2, 3, 4, 5, 5, 6), b = (0, 0, 2, 3, 3, 4, 4, 5, 6, 6), c = (1, 2, 2, 3, 3, 4, 4, 4, 4, 6). (i) Exactly one of the sequences above is graphic. Determine which se- quence is graphic and explain why the other two sequences are not graphic. (ii) Construct a graph that has a degree sequence equal to the sequence from part (i). (b) (i) Compute the Prufer sequence for the tree 8 2 Explain your answer. (ii) Construct the labelled tree that has Prufer sequence (1, 1, 1, 2, 2, 2, 4). (c) How many labelled trees are there with 11 vertices and 6 leaves

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