Can a graph with 11 vertices and 56 edges exist?

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Can a simple graph with the following property exist?

The graph is to have 11 vertices and 56 edges.

Thanks for the help.

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1 Answer

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No.

We can have maximum number of edges in a complete graph.

For $n $ vertices complete graph $k_n$ we have $\frac{n(n-1)}{2}$ edges.

For 11 vertices we can have $11\cdot 10 /2 = 55$ edges. Hence it is not possible.

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