This is part of my Discrete Math homework and I have no idea how to solve this.
I am given this sequence: $8, 8, 7, 7, 6, 6, 4, 3, 2, 1, 1, 1 $
I have to check whether it is graphic or not.
How do I go on about doing that? Haven't done anything like this before so I'm a bit puzzled. I'm not sure how to solve this, do I have to plot this sequence or what?
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 $\iff$
$7,6,6,5,5,3,2,1,1,1,1$ is graphic $\iff$
$5,5,4,4,2,1,0,1,1,1$ is graphic $\iff$
$4,3,3,0,0,1,1,1,1$ is graphic $\iff$
$2,2,0,0,0,0,1,1,$ is graphic $\iff$
$1,0,0,0,0,0,1$ is graphic. So the graph is in fact graphic.
Here is a graph with that degree sequence