# Graph Theory

1. Apr 14, 2008

### saubbie

1. The problem statement, all variables and given/known data

I have two questions. 1.)There are exactly two nonisomorphic graphs with vertex sequence 3, 3, 3,3, 3, 3, 6. Find them.

2.)Does there exist a connected graph with vertex degrees 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3? If there is, then draw such a graph. If
not, explain why not.

2. Relevant equations

I am still unclear as to what a nonisomorhpic graph is. I think that I may have found them, but how do I check if they are nonisomorphic?

3. The attempt at a solution

For the second one, my initial thought is that it is not possible since there are 20 vertexes, and each has degree 3 there will always be two that get left with only degree 2. If there were 21 vertexes, then it would be possible. Any other thoughts or suggestions? Thanks.

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