The line graph $L(G)$ of a graph $G$ has a vertex for each edge of $G$, and two of these vertices are adjacent if and only if the corresponding edges in $G$ have a common end vertex.
(a) Show that $L(G)$ has an Euler cycle if $G$ has an Euler cycle.
(b) Find a graph $G$ that has no Euler cycle but for which $L(G)$ has an Euler cycle.
I just need a hint here.
What theorems do I use to show (a)?
If I can understand (a) I can definitely do (b) on my own