00:01
We are given the degree sequence per graph, and we are asked to find how many edges this graph has, and to draw this graph, or draw an example of such a graph.
00:15
So we're given the degree sequence is 5 -2 -2 -2 -1, and so we have by the handshaking theorem, two times the number of edges, call it e, is equal to the sum overall the vertices.
00:47
Of the degree of the vertices.
00:52
And we have, at the degree sequence, that this is going to be 5 plus 2 plus 2 plus 2 plus 2 plus 1.
01:09
This is 14, and so it follows that the number of edges, e is 7.
01:27
To draw such a graph, first we're going to draw the node which has a degree of a degree of.
01:37
Of 1.
01:41
Call this a.
01:43
And then we'll draw another node to b.
01:47
And we know that a has degree 1, so it's only edge is from a to b.
01:54
Now, the rest of the graph depends a little bit.
02:02
So recognize that we have four vertices with a degree of 2.
02:10
Using these four vertices, we could make a cycle, or we could make instead a pentagon with four vertices plus the vertices of degree five and we'll figure out the rest from there.
02:41
So we have vertex c as well and a vertex d and a vertex e and finally a vertex f...