handshaking theorem

Let $$G$$ $$\,\,\,\,\, = \,\,\,\left( {V,\,\,\,\,\,E} \right)$$ be a graph. Define $$\xi \left( G \right) = \sum\limits_d {{i_d} \times } {\mkern 1mu} d,$$ where $${{i_d}}$$ is the...

What is the number of vertices in an undirected connected graph with $$27$$ edges, $$6$$ vertices of degree $$2$$, $$\,\,$$ $$3$$ vertices of degree 4 and remaining of degree 3?