# Does the graph G' has a Euler circuit?

We have the bipartite graph $G=K_{5,9}$.

We construct a new graph $G'$ by adding a new vertex $u$ that is connected with each vertex of $G$.

Then $G'$ has an Euler circuit, because every vertex has an even degree (the degree of $u$ is $5+9=14$, the degrees of the old vertices in the new graph $G'$ are $9+1=10$ and $5+1=6$ respectively) and $G'$ is connected.

Is this correct? Or doesn't $G'$ have an Euler circuit?