Prove there is precisely one 4 regular graph on 6 vertices.

any advice will help

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- December 9th 2009, 12:42 AMAwesomeDesiKid4-regular Graph
Prove there is precisely one 4 regular graph on 6 vertices.

any advice will help - December 9th 2009, 01:00 AMguildmage
I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?

- December 9th 2009, 02:30 AMAwesomeDesiKid
- December 19th 2009, 04:47 PMkumarstays4 regular graph on 6 vertices.
That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

proof .

consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges. - December 19th 2009, 04:49 PMkumarstays4-regular graph with 6 vertices
That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

proof .

consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.