Nonisomorphic graphs with 10 vertices all of degree 3

In summary, there are 19 non-isomorphic, connected, 3-regular graphs with 10 vertices. These can be found using GENREG.
  • #1
Bingk1
16
0
Hello,
I need help finding all non-isomorphic graphs that have exactly ten vertices, and each vertex has degree three. Does anyone know where I could find them? Or how many there are?
I know that playing around with generalized Petersen graphs gives a few, but I doubt that would give all of them.

Thanks!
 
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  • #2
Bingk said:
Hello,
I need help finding all non-isomorphic graphs that have exactly ten vertices, and each vertex has degree three. Does anyone know where I could find them? Or how many there are?
I know that playing around with generalized Petersen graphs gives a few, but I doubt that would give all of them.

Thanks!

Hi Bingk, :)

If you want all the non-isomorphic, connected, 3-regular graphs of 10 vertices please refer >>this<<. There seem to be 19 such graphs. The graphs were computed using GENREG.
 

FAQ: Nonisomorphic graphs with 10 vertices all of degree 3

1. What are nonisomorphic graphs?

Nonisomorphic graphs are graphs that cannot be transformed into each other by rearranging or relabeling their vertices and edges. In simpler terms, they are graphs that are not the same, even though they may have the same number of vertices and edges.

2. How many nonisomorphic graphs with 10 vertices and all of degree 3 exist?

There are 144 nonisomorphic graphs with 10 vertices and all of degree 3. This has been proven mathematically through the use of graph theory and combinatorics.

3. What makes nonisomorphic graphs with 10 vertices and all of degree 3 unique?

Each nonisomorphic graph with 10 vertices and all of degree 3 has a distinct arrangement of its vertices and edges. This means that even though they may have the same number of vertices and edges, they are not the same graph and have different properties and characteristics.

4. Can nonisomorphic graphs with 10 vertices and all of degree 3 be used in real-world applications?

Yes, nonisomorphic graphs with 10 vertices and all of degree 3 can be used in various fields such as computer science, chemistry, and social sciences. They are used to model and solve real-world problems, as well as to study and analyze complex systems.

5. How are nonisomorphic graphs with 10 vertices and all of degree 3 useful in scientific research?

Nonisomorphic graphs with 10 vertices and all of degree 3 have been extensively studied and analyzed in graph theory, which is a fundamental area of mathematics. They provide valuable insights and help develop new theories and algorithms in various fields of science and engineering.

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