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

## 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
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
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