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Degrees of Vertices I

Joystar1977

Active member
Jul 24, 2013
119
Let G be a graph with vertex set V = {v1, v2, v3, v4, v5}.

Is it possible for the degrees of the vertices to be 3, 6, 2, 1, 5, respectively? Why or why not?

2E = deg v1 + deg v2 + deg v3 + deg v4 + deg v5

2E = 3 + 6 + 2 + 1 + 5

2E = 17

E = 8.5

Is this correct to say that yes it is possible for the degrees of the vertices to be 3, 6, 2, 1, 5 because you end up with the number of edges being a decimal number?

Is it correct to say no that its not possible for the degrees of the vertices to be 3, 6, 2, 1, 5 because you end up with the number of edges being a decimal number?
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
Let G be a graph with vertex set V = {v1, v2, v3, v4, v5}.

Is it possible for the degrees of the vertices to be 3, 6, 2, 1, 5, respectively? Why or why not?

2E = deg v1 + deg v2 + deg v3 + deg v4 + deg v5

2E = 3 + 6 + 2 + 1 + 5

2E = 17

E = 8.5

Is this correct to say that yes it is possible for the degrees of the vertices to be 3, 6, 2, 1, 5 because you end up with the number of edges being a decimal number?

Is it correct to say no that its not possible for the degrees of the vertices to be 3, 6, 2, 1, 5 because you end up with the number of edges being a decimal number?
The number of edges in a graph cannot be other than a whole number. Thus there is no graph possible which has vertices of degrees 3, 6, 2, 1, 5.