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

#### r0bHadz

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??

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#### QuantumQuest

Science Advisor
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.

• WWGD

#### 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

Science Advisor
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.

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