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How many non-isomorphic simple graph are there with N vertices, where N = 4 ?

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Maximum number of edges possible with 4 vertices = $\binom{4}{2} = 6$. So, we take each number of edge one by one and examine.

The possible non isomorphic graphs with 4 vertices are as follows. All other possibilities you may think of, are isomorphic to one of the following graphs.

Answer: 11

Pardon me for the drawings.

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Answer should be 10. 

Since the number of vertices is 4, the maximum number of vertices can be 6.

With 0 edges - 1

with 1 edge -1

with 2 edges - 2

with 3 edges - 2

with 4 edges - 2

with 5 edges - 1

with 6 edges - 1

If anyone finds any mistake in my answer , please do mention it in the comment.

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