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

Problem 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??

Related Precalculus Mathematics Homework News on Phys.org

#### QuantumQuest

Gold Member
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.

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

Gold Member
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.

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

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving