Question

Is the sequence S = {9,8,8,7,7,6,6,5,4,2} graphical? Justify your answer.​

Answer 1

Explanation:

7

Down vote

Accepted

A sequence is graphic if and only if the sequence obtained by deleting the largest degree k and subtracting one to the k largest degrees remaining is graphic.Try to prove this by induction.

hence you get 8,8,7,7,6,6,4,3,2,1,1,1 is graphic ⟺

7,6,6,5,5,3,2,1,1,1,1 is graphic ⟺

5,5,4,4,2,1,0,1,1,1 is graphic ⟺

4,3,3,0,0,1,1,1,1 is graphic ⟺

2,2,0,0,0,0,1,1, is graphic ⟺

1,0,0,0,0,0,1 is graphic. So the graph is in fact graphic.

Here is a graph with that degree sequence

Answer 2

Explanation:

the solution is given in the attachment , review and clear your doubt