How many nodes of each degree are there in this graph?

[r0bHadz]

Homework Statement

A graph has 12 edges and 6 nodes, each of which has degree of 2 or 5. How many nodes
are there of each degree?

Relevant Equations

handshake theorem.
2m = summation of degree of each vertice where m = # of edges

there must be an even number of vertices of odd degree, and from the handshake theorem, 2m = 2(12) = 24

the only way we can get this from 6 vertices using 2 and 5 is:

4 vertices of degree 5, 2 vertices of degree 2

does this seem correct??

 

[QuantumQuest]

If we denote with $x$ the number of nodes with degree $2$ and with $6 - x$ the number of nodes with degree $5$ then according to the theorem you say, you have a simple equation of the first degree in $x$.
Its solution gives what is asked.

 

[r0bHadz]

If we denote with $x$ the number of nodes with degree $2$ and with $6 - x$ the number of nodes with degree $5$ then according to the theorem you say, you have a simple equation of the first degree in $x$.
Its solution gives what is asked.

So do I just plug and chug to find out? It seems like 4 of degree 5 and 2 of degree 2 meets the requirements?

 

[QuantumQuest]

So do I just plug and chug to find out? It seems like 4 of degree 5 and 2 of degree 2 meets the requirements?

I would say yes, it seems so, but you must first form the equation and then solve it, in order to see it.