Chapter 10.1, Problem 20E

To determine

$G_1$ and $C_1$ have a vertex in common. Suppose that $C_1\left(v_1{\epsilon }_1\right)$ is a circui9t in a connected graph G that does not contain all the edges of g. Let $G_1$ be the sub graph of whose edge set is $\epsilon \backslash {\epsilon }_1$ and who’s vertex set is v less those vertices of $v_1$ that becomes isolated after the removal of the edges in ${\epsilon }_1$.