Please consider this graph

How many non-Isomorph trees with 4 vertex has this graph?
Is there any formula that show number of non-Isomorph trees with $n$ vertices?
thanks
Please consider this graph

How many non-Isomorph trees with 4 vertex has this graph?
Is there any formula that show number of non-Isomorph trees with $n$ vertices?
thanks
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There are only two 4-node trees up to isomorphism: the straight line and the Y-shaped graph. The above graph contains both of them.
For the number of trees with $n$ vertices, Wikipedia links here : http://oeis.org/A000055 .