use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph (without drawing the graph) a graph with 4 vertices, each of 2 degree 2
[tex]\begin{gathered} \text{Handshaking theorem} \\ Sum\text{ of degre}e\text{ of all the vertices=2}\times Number\text{ of vertices} \\ So,\text{ } \\ n\times2=2\times4 \\ n=4(nu\text{mber of edge)} \end{gathered}[/tex]
